BTW, I have taken lessons. One of the problems of taking lessons is your taking advice from someone who may not play the way you do.
Okay, I'm going to be a bit harsh and to the point here, but I'm not intending to offend you.......so take that however you want.
No. The "problem" with taking lessons is that YOU don't know what you're doing and the teacher (hopefully!) does. Turf had some great (and funny) analogies, which are all true! Again, no offense, but you're a beginner and to most of us, that means we truly don't know what we're doing. We've all been there. I know I certainly have. I'd wager that any legitimate saxophone teacher (not someone who was self taught but you think is "good") could and would set you straight about this whole fingering fiasco within 3 minutes of your first lesson. I assure you I would. That's not being mean or "not the way you do". It's the CORRECT way.
I'll close with this. Feel free to do whatever the heck you want, but if you're wanting to progress beyond beginner status, the first thing you need to do is how to finger notes correctly. Yeah, some are a pain at first, but just like anything else, doing it that way for as little as 10 minutes straight will fix the issue. The big problem with bad habits is once you do them for a length of time, it becomes incredibly difficult to change them. Again, ask me how I know!
Oh, and the reason alto and tenor react/sound differently is because they're two different sized and pitched instruments. MANY notes on alto don't sound or feel the same on tenor (literally and figuratively). One last analogy. Comparing the sound of alto to tenor is like comparing the sound of a lawnmower engine to a V-8. But they're both engines....... ;-)
The end.