To play a weak engine competitively against Big Money, you need a means of slowing your opponent down enough to give your engine time to fire. Which typically means having an Attack. There are Attacks other than cursers, definitely, but cursers are frequently great for this purpose - most of them also provide some halfway decent bonus to an engine, and since a BM player likely hasn't grabbed a deck thinner the Curses are highly likely to hinder them (compared to, say, a discard attack where the BM player may well be playing BM-big draw, or just has enough rubbish cards in hand to discard anyway). So without cursers, you have fewer games where you can make an engine work.
Another interesting consideration - if there were no cursers, would people be more or less likely to discover the power of thinning in the first place? A common progression that you hear from new players goes something like this:
1. Chapel is only there to trash Curses, so if Witch isn't in the Kingdom then I don't need Chapel.
2. Actually, since I can trash so many cards with Chapel, I wonder what happens if I trash the Curses *and* some of my starting cards?
3. Wow, my deck gets so much better when it's thin and filled with good cards rather than fat and filled with Estates and Coppers!
4. Maybe I should buy Chapel to trash my starting cards even if I *don't* have Curses.
5. Chapel is amazing!
If you just had the base set with no Witch and no Curses, how many players would just keep ignoring Chapel? How many would think "Why would I want to trash stuff?" and jump to step 2? I suspect that there are a few people, mostly serious gamers, who would see Chapel and realise the value of a thin deck, but so many more players would just see Chapel and play a 9-card Kingdom.