Returning champions:
The primary two reasons for Wheel's adoption of "no returning champions" (aside from their occasionally pulling the Friday Finals out of mothballs for a couple of themed/celebrity weeks) were 1) Sajak's stated preference against champions (he's noted it in an exhaustive number of interviews), and more importantly 2) allows the show to consolidate the number of taping days from 39 to, as of season 41, just 34. (five weeks of episodes contain shows taped at prior tapings but then aired together). Cutting five taping dates saves on studio time, crew expenses, and more, while spreading out other costs over six shows instead of five.
One of those reasons is now gone, however, to add champions back you also have to likely reinstate those five tape dates. Does the benefit outweigh the cost? Especially in the current TV landscape and the death valley that is the syndication market? For three or five day champions with a limit, the argument is almost assuredly no. For Jeopardy-style unlimited tapings? It's arguably the best change the quiz show's ever made (see: ratings bump for and source of eventual host Ken Jennings, ratings bumps for Holzhauer, Schneider, et al., with it increasing J!'s social media buzz immensely). Wheel doing that, even if it's a more luck-based game, could be an injection of life into the show that justifies the added costs. If they're going to do it, they need to go all in.
Rest of the show:
I despise the Prize Puzzle as it's currently implemented. If they insist on keeping it, it should never ever count as "score money", as the other poster noted using the Pyramid term.
I actually really like the Triple Tossup, especially once it occurred to them to start linking the three puzzles together thematically. I also like having the initial play-in one. Not crazy about the "you get to be interviewed first, and here's $1K" opening one. I'd nix that, bump the other opening one to $3K, and winning it controls both the interview and control for R1 - which I actually liked the one year they did it that way.
They have got to get over their allergy to four-digit wheel values (or at this point, anything outside the $500-$700 range). Low dollar should be whatever the cost of vowels is, and there should be a nice spread up through approx. just over of whatever top dollar is. If R1 is $2500, throw a pair of $1000s, a $1250, and a $1500 on the wheel. R2 for $3500, add on $2000. When you put $5000 on the wheel, add $2500 back. Once you know the puzzle now, there is basically no incentive to spin again and risk it, especially if it's the prize puzzle.
I love the way that the Crossword and Same Letter categories reward having to think about the puzzle slightly out-of-the-box, and I'd love to resurrect categories like Clue and Fill in the Blank that require a little bit of extra-dimensional thinking.
I liked the Free Play wedge, but if it's gone for good, at least bring back the Free Spin token. One of my favorite part of watching shows from the 80s, especially as someone who loathes the shopping round, was watching someone occasionally managing to bank an absurd number of free spin tokens, so if they wanted to go all in on a free spin *wedge* again I wouldn't even mind.
Wild Card should be able to be used for vowels in the bonus round. It should be able to be automatically exchanged for top dollar in the main game since that's the only time people use it anymore, with the catch that if the letter you call with it isn't in the puzzle, it counts as a bankrupt instead of a lost turn.
As much as people don't like to go on game shows to win things outside of cars/cash and occasionally trips, I REALLY miss Wheel's more eccentric prizes and prize packages of the 80s and 90s. I'd love to see them get back to those, with the possible tradeoff that every prize except the cash itself now comes with a base level of cash. ("And for gas money, we've stocked the trunk of this Volvo with good ol' American cash, FIVE THOUSAND DOLLARS!"). Pair that with champions and it's a lot more interesting.
For it's faults, the shopping era - and the vastly superior IMO first decade-ish of the cash format - had this whimsy that the show gave up in the late 90s in the name of a more efficient production. I'd just love to see the show try to recapture that.