The new way is better, and it's not close. The only thing I miss from the old days is the ability to preserve each individual old version and old meta, whereas these days we just update the new version on top of it. If you're the kind of player who felt like Happy Chaos ruined Guilty Gear Strive, you can't really go back to a version before he existed. Up until this latest patch, I felt like the best time in the game's lifespan so far was right before Happy Chaos launched (for reasons beyond the state that Happy Chaos launched in). Thankfully, this new season is great, but we might not have been so lucky.
People outside of the fighting game sphere would perceive these new games as a "rip off"
I'm going to wager plenty of people inside that sphere would consider them to be a rip-off as well. Super Street Fighter IV didn't change any more about characters' gimmicks than your typical seasonal update does in modern games. They had limited ability to patch games back then, and the new boxed copy was all they could do, but this new method allows them to demonstrably keep a larger pool of players online playing the game than the old method did, which provides more value to future purchasers, which theoretically drives more sales before we even get into the economics of Street Fighter costumes. I know when I bought Guilty Gear Xrd Sign, I wasn't too compelled to pick up Revelator when it came out, since it appeared to be barely different from the version I already had, and no one was really playing that previous one online anyway.
An example would be Super Street Fighter IV launching with 10 new characters and 5 new stages for 40 dollars -- a price that is basically in-line with modern "seasons" in the worst case scenario and it can be debated that it was actually a great value when you consider all of the additional work and polish to other UI and gameplay elements.
That's $40 in 2010 money. It would be more like $56 in today's dollars.