You are dead on, O.P.!
First thing to know about the ground beef you buy in most stores is that it's all from used-up dairy cows. And it's from EVERY PART of the cow that couldn't be carved off the bones and labeled as something else. That's why it tastes different from fresh-ground table-beef chuck, for example....and also the reason it's so risky in terms of contaminants like E-coli. The meat in that tube can have come from the mix of scraps from hundreds of cows, and every step in that process is an opportunity for pathogens to be introduced.
I won't buy such "beef", unless for something that's going to be cooked to death like spaghetti sauce, tacos, or meat loaf.
For pure patties/steaks/tartare, I insist on fresh-ground from identifiable cuts off a TABLE BEEF BREED.
Walmart may be an exception in the "we won't grind" department...my local Safeway/QFC/Fred Meyer's/Albertsons all have butchers that will grind any beef cut to one's specifications. Look around locally- not every chain follows Walmart's lead.
For home grinding, here's my experience:
I used to have an oldie like you describe and it worked great. Thinking I'd like something more "powerful", I discarded it in favor of a big ol' honkin' unit from Cabela's that looked really impressive.
But it turned out LOUSY ground beef. Unlike the older unit, which had blades that really cut the meat, the newer unit sort of squished/extruded it in a sort of unpalatable mush. Yuck!
If you're satisfied with the look/feel of the grind you're getting from the old unit, hang on to it!