I think a key thing missing in this discussion is a) how would you prefer the Celtics spend the money, and b) how much money would signing IT to a large contract actually take up?
Suppose that the Celtics are able to sign a max free agent this summer at the 7-9 years experience level. Suppose we also get another top 3 pick from the Nets. That max free agent will make about $30 million in 2018-2019. The draft pick will make approximately what Jaylen Brown is scheduled to make. Let's also assume Rozier gets to stick around, but for the time being forget about all of our other draft picks, be they stashed, on the roster, or in the future (like the 2018 Nets pick). That would leave us with 6 players under contract:
Horford
Mystery max player
Crowder
Brown
Rozier
Nets 2017 pick.
Just those six players cost about $80 million. Already you've run out of room for another max player. You can pay a single guy a lot of money, but not the max.
But also, we've assumed that we let Olynyk walk next year, and we're also letting Smart walk in this scenario. Keep one of them and you're over $90 million committed to 7 players -- now you've just got role player money left. Keep both of them, and you're probably capped out. And I didn't even mention Bradley, who would carry a cap hold of at least $13.2 million himself. And again, there are probably some draftees, either currently on the roste or yet to be taken, who will carry additional cap space also.
So in this scenario, it really becomes a decision of going a good deal over the cap to retain IT, and maybe even touching the luxury tax, or letting him go. You're not replacing him with a free agent. He's just gone. And this is where the "it's not our money" argument comes in. Is it better to pay IT $20, even $25 million, or just fill the roster spot with a second round pick?
Alternatively, suppose we don't hit on a free agent next summer. Now you probably can get a max free agent, if one will come. And yet, in a world where we have cap space, IT would have a cap hold of $11.9 million. The max salary will again be around $29 million. If a max player could fit into the Celtics along with IT's cap hold, wouldn't you want to keep IT? You're not going to get someone to replace him for $12 million. Look at this year's salaries, factor in another $10+ million of the cap rising, and it's just not happening. Again, if you're going over the cap, does it really matter if IT is paid $15 million or $25 million, if it isn't your money?
I think people have grown too accustomed to the Celtics having large amounts of cap room. That's going to end soon, probably after next summer, maybe before then if a trade occurs. Possibly 2018. But it's ending, if for no other reason than some of the draft picks will have become long-term players to be kept, and accordingly their salaries will rise -- specifically Olynyk and Smart. And if IT is being paid a ton in 2019 and 2020, when we aren't going to have cap room any way, what does it matter, if it's not our money? Sure maybe the Celtics will decide it's not worth the luxury tax (although the higher the cap goes, the wider the gap between the two levels, so that might not be an actual comsideration). But from an opportunity cost of cap room, it's unlikely IT getting paid big time in the future will have any real negative impact. There is a narrow range of possibilities that makes IT's cap hold prohibitive for a max player in 2018, but narrow is the key word. It's highly unlikely we're significantly under the cap in the years beyond 2018, regardless of IT, until either another rebuild occurs, or there's a significant change to the cap again.
Remember, we were pretty much over the cap for the better part of two decades. That's the norm, not these years in the recent past and near future.