Whether or not a PS2 game supports progressive scan is the developer's choice. Many of the more popular games in the last couple of years do support it, but there are a lot that don't also. There doesn't appear to be a way to magically enable a progressive mode for any given game that wasn't coded for it, or else I'd expect to see mod chips or boot discs for this purpose already.
As for the DVD movie progressive issue, it is probably a firmware thing. How determined you are to replace that firmware may reveal how difficult it is, or if it's even worth desoldering one console's chip with the firmware resident. (I'd say it isn't, but then I know you like to hack.
) Also, if you have an older PS2, it will still display the games progressively, assuming the game in question was coded to do it, the 5000x model only added a progressive movie player.