Quite odd, because the other AIs seem to do fine. The AI is even techrushing philosphy techs in my games, and I recently saw France start colonizing in August 1870. 
The AI never selects the right techs !
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Considering that the boost from philosphy is tremendous, I can think only of few scenarios where you want to forgo an instant research:
(1) You want to colonize ASAP. That is - in fact - a good reason to skip Analytic Philosphy in 1870.
(2) An upcoming important war. Either you rush an army tech and try to steamroll the enemy (Military Directionism, Machine Gun, Bolt-Action Rifles) or you are an underdog and know that the AI is coming for you. Then it is necessary, but still not preferrable.
(3) You skip Idealism because you want Ideological Thought first, since the plurality boost gives more RP and the additional benefits are nice. A valid reason, imo.
But considering that each level of philosphy is roughly a ~20-30% boost to your available RP, it will usually pay for itself within 5-10 years. So there is almost no reason to not research it asap - and absolutely no reason to stay more than one level behind!
If you are short on money, cut funding for a few years until you have another power tech. Hell, even go in debt if you need to, but don't skip philosophy for money!
Plus: There are only very few techs that you really need to rush. A thing I learned from my AHD games (roughly 30 finished ones so far) is, that the industry techs do NOT need to be rushed. In fact, most of them are rather weak. Electricity and Combustion sounds nice on paper, but you will lack rubber to start producing significant amounts of goods. And once enough rubber is available, other countries will already start to build some factories. And the most profitable late game factories are in fact not in the industry tree: Commerce has Synthetic Oil (a real moneymaker!) and Culture has Radios. Both have low ressource input requirements while their outputs sell like sliced bread.
The only techs that are really more important to rush them are Machine Guns for colonizing, Military Directionism for Gas Attack roflstomp (although that is more like a gamble) and Management Strategy to hurt the economy of your enemies badly for a few years.
Well, that is the difference between us. I usually think about how I want my country to look around 1900, so why should I care about short term issues in 1870?
Apart from that:
(1) Industry mostly boosts RGO, while commerce boosts factories.
If you want to play an agricultural Russia, go for industry. Otherwise: Just research enough industry techs so your treasury is evened out and then switch to Commerce Organisation.
But while money is short during the early game, it is mostly not an issue after 1850 unless you have a huge army or plan to build an enormous DN fleet. In fact: Money is mostly useless in this game for any decent sized nation.
(2) Philosophy has a lot more benefits than just more RP.
Remember that in these 8 years, you will aready benefit by having more daily RP, thus other techs are finished faster and their benefits apply more quickly as well. There is a HUGE difference between 700 and 500 days of research for a tech.
So even if you want to rush army techs, it will only take 3-4 years until you have again reached the same tech level vs. a person that has skipped the tech. Plus, as you mentioned: Prestige.
Short calculation:
Tier IV techs for 14.000 RP. You have 30 RP/d, with Analytic Philosophy you get 40 RP/d. You save up one year of RP in 1869 (10950 RP).
The first tech will be finished in early April 1870. Now let's compare the situation for army tech vs. AP + army tech:
April 1870: 1 army tech vs. 0+AP.
April 1871: 1 vs. 1+AP.
July 1871: 2 vs 1+AP.
April 1872: 2 vs 2+AP
November 1872: 3 vs 2+AP.
March 1873: 3 vs 3+AP.
February 1874: 4 vs 3+AP.
March 1874: 4 vs 4+AP.
Russia has no need for expansion. It has already so many pops - why should you pay a costly war and risk upsetting other GPs for a few hundred thousand more people that may not even be of your culture?
In fact, in SP, most nations you play do not need to wage a single war and still can be #1 in 1936. That's the beautiful thing with Vicky 2: You can warmonger if you want, but the gameplay does not make war that benefitial.
Okay, certain goods like tropical wood, rubber and oil can be worth a war to be directly under your control, but most of the time you can sphere the nations that produce it.
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Philosophy is a no brainer that pays for itself within 3-5 years, maybe apart from very few certain circumstances, like starting colonisation or plannung an offensive war with tech advantage. So the AI should really research it asap (apart from 1870). Education techs are another thing, esp. for large nations like Russia.
The problem is that you can only weight techs, so there is ALWAYS a chance that the AI will chose something else. What might help to solve the problems, though, would be a tech check. So for example, if the AI does NOT have the tier II power tech, it has a much smaller chance to research other tier III techs from the tree.
Another problem is, that the player can exploit the AI if it has a too obvious research pattern. In HoI2 you could assign different building templates to nations, so for example in one game GER did built a submarine fleet, in another it built a surface fleet, in another one there was the chance it would build a CV fleet and in a another game it didn't build any navy at all - so no game was always the same. However, the AI in AHD is quite predictable - and if the AI would focus on the strongest techs too much, it would become even worse.
The ideal thing would be a reactive AI that "learns" during the game, but that is probably extremely difficult to script with the given system. For example, most of the time as Chile, you can sit back cause nobody will attack you. You can even disband most of the army and forgo army techs, giving you a huge early game advantage that will become an even greater late game advantage. Now if the Argentinan AI would become smarter after it has seen Chile sitting around with 3 brigades for 20 years, it would start teching some land techs, build a few more units and grab that ripe Chilean territory.
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There are really only two no-brainer techs for the beginning:
(1) Ideological Though (for pluralism + NF).
(2) Idealism for RP boost.
Unless you expect a war within the first 5 years, these shoudl ALWAYS be the first two to research.
But from that point on it really depends. I agree that education techs are really neat, but additional NF early on allow you to promote up to 4% clergymen fast, which is WAY more powerful in terms of literacy increase than researching the early education techs.
One should try to grab Biologism fast, but I guess even that 50% boost is less worthwhile than the early NF.
As for the higher tiers, I agree partially. The NF techs beyond N&I are not too great. But: They are in fact reducing rebel power until fascists kick in - and only failing nations will have to deal with those anyway.
(1) Ideological Though (for pluralism + NF).
(2) Idealism for RP boost.
Unless you expect a war within the first 5 years, these shoudl ALWAYS be the first two to research.
But from that point on it really depends. I agree that education techs are really neat, but additional NF early on allow you to promote up to 4% clergymen fast, which is WAY more powerful in terms of literacy increase than researching the early education techs.
One should try to grab Biologism fast, but I guess even that 50% boost is less worthwhile than the early NF.
As for the higher tiers, I agree partially. The NF techs beyond N&I are not too great. But: They are in fact reducing rebel power until fascists kick in - and only failing nations will have to deal with those anyway.
They are province based, so they are really neglectible for most medium-to-large sized nations.