Well, as a tag team, they are pretty irrelevant. Sure, they have fun matches, but they are nothing special. There are PLENTY of high flyers and spot monkeys. They are better than most, but they are not special. They suck as characters and their matches are spotfests. Well done spotfests for the most part, so I am willing to have them in the conversation of best tag teams of the 21st Century even though they would be pretty low in my top 10.
Now, if you want to talk about influence on the BUSINESS itself, then, yes, definitely, 100% the most influential. They basically took over ROH, they did All in, they were instrumental to the creation of AEW. They also revolutionized merch in a way. They did A LOT on the business side and they also did a GREAT job marketing themselves as way more important/talented than they really are. At the end of the day, being able to sell yourself is a VERY important component of wrestling and I think they have been the best at it especially pre-AEW.