I still think the most important thing is the caliber of player of the type of player. An interesting spot to look at is Ingram. It seems like most of the league is skeptical about giving him a full max, otherwise he'd have a much bigger trade market. While no one seems to want to give it to him right now, it seems as though he's holding out thinking he will eventually get one next summer. He's a great example of a guy who would be a no questions asked max guy in the last CBA, but not this CBA. I think David Griffin has actually come out and said that Ingram would have been full maxed in the old CBA.
Ingram is a popular trade idea around here....but it makes you think, what is the Jazz situation like with Ingram and Lauri on (close to) max contracts? I think that in the previous CBA, you could feasibly see small market teams like the Jazz having 3 big contracts on the books. Nowadays, I don't think that's possible unless you're really barebones around those three guys.
Anyways, back to your question...I think it's easier to start the conversation with who is obvious. The elite of the elite are obviously no brainers. I also think guys who consistently make all star teams are no brainers. Guys like Mitchell/Booker who aren't necessarily elite but are most likely going to make the all star team are no brainers. I think guys the are borderline all star is an interesting conversation. I think for the most part they will always find teams to give them a max, and therefore it will take a max to keep them. Guys like Lauri/Fox are in this category. They will yield a max (or close to it).....but I think those contracts come at some non-zero risk of turning into questionable. As long as they maintain their status/level I think their contract will be considered highly desirable. But any slippage there and you might fall into the Ingram zone. It's not likely that a player in his prime years slips off, but like I said, there's some non-zero chance of that happening.
Another situation that I know people are getting curious about is Jamal Murray. He hasn't signed an extension to the surprise of many. Is that a situation where DEN is going to try to play hardball and get him at less than max? Is he a max player? That's a situation which would be no brainer last CBA but not this CBA.