Biggest reason is MLS salary cap has limited the talent that any MLS team can actually have. MLS teams (not all owners care) have gotten more talented over the last 5 years and closes the gap in talent, but Mexico without having a salary cap can build a better team.
Another reason MLS has faired so poorly is because Champions League is usually going on in the spring when MLS season is just starting. Meanwhile Liga MX teams are more in form as their season has been going for awhile.
Seattle though made it their priority and mission to win Champions League. They are struggling in the early stages of the MLS season as they’ve been resting stars and playing role players. All you have to be is in the top 7 to make the MLS playoffs and from there anything goes. So a team like Seattle who is seeded 5-7th can do damage in the playoffs and still win the MLS championship even with their early Champions League distraction.
in addition, a lot of teams in the past didn't really emphasize the competition because they didn't know how to market it to their fanbases, attendances used to be horrible, and they were knocked out early anyway.