The T3 is head and shoulders better than your point and shoot pocket Canon cameras. The pocket cameras aren't all that bad depending on which one you get. I've taken what I think are some great photos with them. The high telephoto lenses on some models will affect image quality IMO. But with the ability to change lenses and better lenses overall the IQ on the T3 doesn't suffer nearly as much.
I'm not out to make money with my T3. I don't expect to win any contests either. But there is a market for a camera on the level of the T3 clearly. Someone must be buying them. As for them not getting a lot of love on a board like this you have to remember that most of the people here are more serious about photography than I am. I have much better quality video cameras BTW. That is something I do to make money or I did for a good while. I've pretty much quit that too until computers get fast enough to edit HD video the way I want. I don't like waiting all night for a single edit to be put together. Even so my video equipment takes better quality stuff than many HD cameras do. The lens and the sensor makes a lot of difference. And one of my cameras shoots 16:9 video too.
My point is that there is a rear for every seat as my dad used to say (in a more "colorful" manner). If the T3 is your thing don't worry about what anyone else thinks. Remember too that there will always be someone to tell you that if you had just spent a little more money you would have been so much happier and you must have been crazy not to. That applies whether you buy a used Barbie camera (I have one for sale if you're interested) or a EOS-1D X. There's always something more you could have bought and if not wait a week and there will be.
Buy the camera you want and be sure to leave some money for lenses in your budget. Then don't worry what anyone says about it because someone will always look down their nose at you no matter what you buy. I haven't even mentioned Nikon and Sony and Panasonic camera lovers. They will have plenty of criticism for you. I bought what was considered to be one of the best prosumer video cameras on the market but within 6 months it was considered obsolete. Keep that in mind too. Your T3 would have been a super camera about 5 years ago. And I still have still cameras from 12 years ago that take great photos even compared to my T3. I made 8 X 10 prints from a 2MP camera. People said it wasn't possible to do that with less than 5mp then a year later it took 8mp then 10mp and according to some I can't do it with my 12 mp camera either. I wish they could see the photo I took of my father in law that I took with that 2mp camera. He died in 2002 and that photo is worth it's weight in gold to me and my wife. And I would defy anyone to tell me it isn't a good photo if they actually saw it. It has no pixelation even on his white shirt and very little noise too. Don't let people harsh your buzz in other words. The T3 will take some fine photos.
I agree as well.
I'm not a fan of the T3, I think Canon made a boneheaded choice with the alphanumeric naming (came out near the T3i release so it is confusing), and it is really a bare bones Rebel that is way more crippled than it needed to be. The T2i, or similar, (should be the "base" model). The finish on the T3 is cheap in comparison as well.
HOWEVER, that is in comparison to other Canon DSLRs. In comparison to a P&S, it is going to be head and shoulders better. The sensor alone gives you SO much better ISO range, and of course you get all of the convenient manual controls DSLRs have that make P&S's difficult in manual mode.