Austria does not want _everything_, but bohemia is a nice cluster of provinces and can usually be taken with cores, quite useful overall.
They might later be, though.
Its not "all they want", but if you dont give them their landbridge the will have designs on your lands they otherwise might not have, and even without the landbridge they can seriously threaten you, especially if there is no mamlucks player.
So because neither Austria nor Russia can threaten you in the first 10 or 20 years its fine to make sure both hate your guts if they survive? Suuuure, also why the heck should the OE let you do such a thing? You also completely ignore the northern German player and the Scandinavian player who both usually have designs on your baltic lands, so you are surrounded by nations that dont want you to live.
Why would they ally you? I see little benefit as Austria in becoming a quasi polish vassal when you WILL be more powerful than them even without Bohemia. They got 4 Gold provinces while you got none, they got easy acces to trade, which gives them an incredibly strong Ecconomy while poland can never really catch up. Also they have much better and richer lands, which in combination with emperorship gives them higher Forcelimits and more manpower, so dont underestimate Austria.
Well, if you remove bohemia from HRE, they will have no reason to conquer it(non-core land for 36 infamy?). And actualy poland can catch up with tech if you westernize, and take good slider moves. But of course, you can just conquer land around austria capital if you are strong enough, then force them to release vassals, and then just annex them.
But i think leaving austria alive, if you ally them is good, because you won't have to deal with france for example(or milan)
And no, i do not underestimate emperor. Certainly if a very good player plays austria, if you tried taking bohemia without succeding, you can just change your attitude, and offer them alliance, and go conquer russia, and golden horde.
But Ottomans without landbridge, can be taken down much easier than with it(just ally with venice and austria, then stomp them (first in greece, then in asia)- with landbridge it is not so easy). And ottomans are so going to be pain in the butt if they ally with russia for example. Also, you can just offer them pass thru your lands instead of landbridge(this will make ottomans not to attack you, because he won't want to lose his passage, even for the risky attempt for landbridge. So if you can stop ottomans from getting landbrige, it is better for you. If not, they might be not interesed in you, but they may be, just for some nice provinces like kiev...
You say to me, how to play as poland, but i know clearly how to do so. You say me to stay small, weak and don't piss anybody off, but i say i want to become strong nation. And as poland in mp, you just can't do it, without pissing someone off (i mean, at least russia will be allways your enemy).
And austria do not start as emperor, so if for example burgundy will become emperor, they got a problem.