Every American domestic league has trade deadlines in place though they tend to be less limited than the 2 windows most soccer leagues have.
But I think in part the idea is the same - to put some limitation on the ability of teams to rent players for season ending pushes to qualify for regional play, or avoid relegation. With a few dozen major-ish leagues with different schedules, a truly international market, plus a strong cultural norm that players can move whenever they want for fair compensation to their current team, allowing transfers whenever would be a bit too chaotic.
Fans would really hate losing players with a few weeks left in a season just because some bigger club is making a push and offered both player and team a basket of cash. It's bad enough dealing with it in prescribed periods.
I'm no FIFA defender, but I think they get this reasonably right. I understand there was a different system earlier where transfers were allowed year round except for near the end of each season, which sounds similar to the American norm. I think that could work as well. Right now, MLS has less than 25% of the season left for most teams. If that would not put us in the no-transfer zone, it would be close to the deadline under any system but the free-for-all.