It's a "battle" that's just getting started. The US knows crypto is a "force to reckon with", so it's doing everything in its power to minimize its usage across the country. Otherwise, that would mean the death of the US Dollar. DEXs were created as a response from governments' abusive overreach towards crypto users. They might be slow and expensive at times, but no single entity can shut them down thanks to the way they're designed (unless they're not truly-decentralized).
Tightening regulations from the SEC will result in a massive exodus of crypto companies from the US to other areas. US-based crypto customers will be the ones mostly affected when they find out how difficult it'll be to get in/out of crypto with US Dollars. P2P exchanges would be the only way to buy/sell crypto with USD. DEXs don't have Fiat on/off ramps, but they're still useful for crypto-to-crypto trades. I really hope crypto advocates win in the long run, leaving the US open for crypto business. No one can predict the future, so we can only hope for the best. Just my thoughts