This is not 100% true. I have to buy cheapest available for my routes, so that means an L or some other super-discount fare every now and then. I flew AA MCO-DFW/DFW-DCA a couple months back. I only paid ~$150 for each segment on a pretty low fare class, but was definitely going to upgrade on the MCO-DFW when offered, though I ended up stand-by on the earlier flight instead (and had a great exit row with tons of legroom).

Again, these upgrades are only offered after all elites are accomodated (save a very late arrival into the gate area), so I do not think it will have a negative impact on elite upgrades.