They're the ones training "base" models. There are a lot of smaller base models floating around these days with open weights that individuals can fine-tune, but they can't start from scratch.
What legislation like this would do is essentially let the biggest players pull the ladders up behind them - they've got their big models trained already, but nobody else will be able to afford to follow in their footsteps. The big established players will be locked in at the top by legal fiat.
All this aside from the conceptual flaws of such legislation. You'd be effectively outlawing people from analyzing data that's publicly available to anyone with eyes. There's no basic difference between training an LLM off of a website and indexing it for a search engine, for example. Both of them look at public data and build up a model based on an analysis of it. Neither makes a copy of the data itself, so existing copyright laws don't prohibit it. People arguing for outlawing LLM training are arguing to dramatically expand the concept of copyright in a dangerous new direction it's never covered before.