You can only get so much quality out of a standard TV, yes. There are technologies and connection types that work to get the most out of new and old TVs, but you just can't get a progressive picture on an interlaced-only TV. The DVD player is responsible for having interlaced output, and if you set your DVD player/Xbox/whatever to send progressive output, your display will go nuts. I know, I wanted to see what it would do if I set my Xbox dash to progressive. I'm sure some high high end TVs can do 1080p, but my point was that a TV has to have 1080i to be declared an HDTV, but it doesn't even have to support 720p! So you can have an HDTV (and this is quite common) that only does 480p and 480, 720 and 1080 interlaced. Edit: If you were actually referring to a TV like I just mentioned, I suppose a device could convert the image to 1080i, but I don't know how common that is with a typical player. They probably just output in 720i, but I'm not sure.
Also, I have seen TVs that don't seem to do a very good job of handling interlaced output in certain/all resolutions, so interlaced output looks like SHIT on them. My friend's HDTV makes all his Xbox games look like crap when he uses the standard cable, but with component it looks absolutely beautiful, more detail and color than my standard TV even though I have the same connection type. He was actually playing Ninja Gaiden with the regular cables until I dragged him to Best Buy. The friggin screen would blur when you moved around fast.
As for newer compression, yes you'd still need a new player even if you still used DVDs. But the optical hardware could all be the same, players could be made pretty cheaply. Also you could play them on PCs with standard DVD drives, and burn your own videos with existing drives. But if they're gonna move to a new disc, they should still use better compression regardless. The only compromise is the possible inclusion of new HDTV resolution WMV, which if is made mandatory for standalone players, you could burn a fair amount of HD content on a regular DVD. I'd just prefer they use better technology, although HD WMV isn't as bad as some will make it out to be. OMG teh M$ we r LOSE!!117
Finally, yeah you can only make old film look so much better through remastering (until they perfect time travel and cloaking fields).