Saying the Celtics never signed a big time free agent because they never had enough cap space is like me saying I never got to hook up with Megan Fox because I never met her. It's a ridiculous strawman that doesn't address the real argument why it's hard for the Celtics to sign one of the big fish.
First, you have to make the distinction between star FA and superstar FA. Klay Thompson is a star, Steph Curry is a superstar. When people say the Celtics have a hard time signing big name FAs, they mean players in the superstar category. Does that mean the Celtics are a terrible franchise, or that Boston is a horrible place to live? No, of course not. I've never been to Boston myself, but by all accounts, the city looks beautiful, and the Celtics are a top organization in the NBA. What they mean is, close only counts in horseshoes and hand grenades, as on the rare occasion that a superstar becomes available, only one team in the NBA actually gets to sign him, and the overall package the Celtics can offer, while very good, probably isn't enough to win the player's signature in the end.
Now, why do people say that?
That's because pretty much all players, whether they are superstars, stars or bench warmers, value two things above anything else: money and winning. "Wait", you say, "that's precisely my argument. As long as we beat out the other teams in these two categories, why shoudn't we be able to sign a superstar?" Simple, because of the difference between star and superstar.
When Klay Thompson hits free agency, half of the teams in the NBA will offer him the max. He is that good. When Steph Curry hits free agency, every team in the NBA wants to offer him the max. They would bend over backwards, move heaven and earth, and explore every loophole in the CBA, no matter how small, to make it happen. Since you can't offer anything more than the fix max salary, money simply isn't an issue when trying to sign a superstar FA.
That leaves "winning".
"Hold on", you say, "I get the whole money thing, but why shouldn't we be able to put a good team around, say, Kevin Durant? You add Durant to this team, and we're one of the very best teams in the NBA, probably the best in the east." Again, because of the difference between star and superstar.
A superstar is a transformative kind of player, the type you can put on pretty much any team in the NBA, and you would see signifcant improvement. In some way, they bring the "winning" themselves. You put Kevin Durant on the 76ers, and they'd be an instant playoff contender in the east. "That's nonsense", you say, "no single player, no matter how good, can have that kind of impact. It takes a team to win." While that is all good and well, once you sign a player as good as Kevin Durant, it becomes much easier to put strong players around him. NBA players are like gravity, they're attracted by the biggest mass.
That means "winning", while still very important to any superstar FA, simply isn't a very good argument when you're trying to convince these players to sign with you, unless you already are a successful franchise.
What all of this combined means is, that when Superstar X is a free agent, received offers from other NBA teams, had talks with executives around the league, and now sits down to think about everything and come to a decision, the two things he should value above anything else, money and winning, all of a sudden aren't that dominant of a factor anymore, which, in turn, means the other things he values (which are different from player to player) become a lot more important.
Does that mean the Celtics don't have any chance to sign such a player, ever? No, of course not. Considering the specifics of "Kevin Durant to Boston" right now, we might actually be in a very good position to capture his signature. Personally, I would say we score pretty darn high on many of the "lesser factors". Great coach, great GM, great fans, a playoff team, stable organization, enough assets and flexibility to acquire at least one more star to put next to Durant and still have something left. But don't be surprised if it doesn't happen. The odds are still against us.
Just don't give me that crap about "we never had cap space" as some kind of argument that we're actually a free agent destination.