Does Maritime beat Naval in a head-to-head fight ceterus paribus?
That's assuming the idea groups are a in vacuum, is it not? If so, I disagree that you can compare them that way, this isn't like comparing offensive to defensive, we're dealing with two completely different categories of idea groups. You talk about single player balance, so I will compare them that way.
Naval pros:
Ship durability +10%, heavy combat ability +20%, morale +10%, and engagement +10%. All of these are huge, and greatly contribute to your navy's ability to obliterate other navies. The rest are fire/shock pips which are nice and all but are inferior to maneuver pips, and situational/irrelevant things like prestige from combat; +25% galley combat ability in the open sea doesn't help you at all, and if you're invading an inland sea from elsewhere, you're not going to build galleys to do so, you're just going to use your heavies.
Naval cons:
you're using mil points for this, mil points that could be spent on defensive, offensive, quantity, or quality ideas, and quality offers ship durability +5% and naval morale +10%, so you get about 37.5% of the benefits of taking naval, (falsely) assuming all things are equal, plus the important benefits of troop combat ability and discipline, plus much better policies. When was the last time you took a naval policy? When was the last time you took a quality policy?
Reasons to take Naval in SP:
You're about to fight GB within the next 20 years and you can't build enough heavies to beat them with sheer numbers.
Maritime pros:
+2 maneuver, +50% forcelimit modifier, repair in coastal sea zones. +2 maneuver is great, it increases how many ships can fight, increases the speed of your fleet, and increases your chance to capture enemy ships. I'm sure I don't need to tell you that having a bigger deathstack of ships is a good thing, there's a reason why quantity is considered so good. Granted, repairing in coastal sea zones is more QoL than anything, since you can just leave your ships blockading someone and they'll repair, and you don't need to micro them in and out of ports at the tick of the month, and they can repair on the other side of the globe without hassle. The rest of Maritime's ideas are nice for navies, like reduced ship cost and faster repair, but they don't matter too much. In addition, Maritime uses dip points, so it doesn't have to compete with things like offensive.
Maritime cons:
It doesn't actually increase the fighting ability of ships, unless you consider +1 naval tradition to be a combat advantage. Your ships will always be inferior, much like how relying on only quantity as your military idea doesn't make you kill things better.
Reasons to take Maritime in SP:
You want a huge navy that can kill opponents with sheer numbers.
The real problem is there is no reason to take either aside from RP or the niche scenario of needing to go toe to toe with GB because you have no way of landing troops on them, but if you were to take either, you'd be more likely to use dip points on a navy rather than mil points, yes? We need a reason to use navies, period, and currently there isn't one. That's also partly why making Maritime into the galley idea group is a terrible idea - who even uses galleys? Ottomans, Italy, Aragon, Maghreb, Mamluks. Who else uses galleys? Japan? Ming? Both have to deal with the open oceans rather quickly, so the only reason to have galleys would be to defend home, and have a separate navy with heavies to attack, which is just silly. Baltic nations? They have to deal with outside threats like GB, so unless they're planning to keep the galleys at home, and have a separate fleet to attack, just like Japan/Ming, they have no reason to use them. So it really just boils down to the Mediterranean nations. Why on earth would you change an idea group to essentially be exclusive for Mediterranean nations, especially one as niche as the naval version of Quantity? The only way that could work is if you made it so galleys didn't take a penalty for not fighting in the inland sea if you took the idea group, and doesn't that defeat the entire purpose of galleys?