What do you want to do with BTC scripts that you can't do now? P2SH lets you use arbitrary scripts, at least.
I can't find a single reference on them that contains actual details on the computational model because the internet is full of vapid circular search bait, particularly about cryptocurrencies.
The last I checked, the BTC VM disabled most useful opcodes, which meant you couldn't actually make money automatically redeemable for a large number of constraints you would want to impose.
My quick search seems to support that the VM still disables many opcodes: https://en.bitcoin.it/wiki/Script
What specifically would you like to see done with Bitcoin scripts that can't be done?
For various reasons, you probably want to use arithmetic and string operations for encoding certain problens. You could do it in bit operations, but efficiency.
I can't take credit for it -- it's one of those things that was floating around as a usage early on, but the features were killed.