"Heat" does not strike me as an issue. Look at the slim PS2. It's not like it is a hair-width away from melting. Next to an actual PS3 CPU...a PS2 on a chip would not even be a dot on the radar.
"Cost" does not strike me as an issue. Look at the slim PS2- selling at a what, $150? ...and you can be sure it is at a nice profit. The chip is probably a nonissue at this point, compared to the supporting hardware.
My guess is that dropping in an EE sans GS somewhere in the PS3 is a nobrainer.
As far as PS1 game compatibility on my PS2, it works on every one I have, fwiw. It's a very nice feature, because there are the oldies, but goodies that are really nice to come back to, w/o having to wire up a whole other console. Compatibility won't be full-proof whether you are using original equipment on a chip or emulation, either. You could do either, and there will still be games that won't behave. It entirely depends on the developer and how "by the book" they made their game. Sometimes it is completely out of the control of the developer. Maybe the game runs as it is expected, and to the coder it seems it is running properly, but unbeknownst to all, there may be a bug that relies on errata in the original hardware to run "properly". Some things are going to work, and some aren't. Mostly everything does, so that ends up being a perk.