Oh, ok, you're right then. The Doors were too iconic for Manzarek, Densmore and Krieger to really ever have a chance at anything else. Continuing the Doors didn't work in the absence of their charismatic frontman and house poet, the two post-Morrison Doors albums are not essential purchases to put it mildly. And they never had or did not take the offer to play in another established name band.
Actually, not such a rare thing: Unless you are the perceived leader and chief writer, having similar success in two name bands as a musician is seldom. I guess Frampton did it coming out of Humble Pie (as did Sting departing Police), but even the guys in a mega-band like Purple couldn't continue on a similar scale. Jon Lord almost had an offer from Bad Company after Purple split, but was vetoed by Paul Rodgers who didn't think a dominant Hammond sound was the right thing for the nearing 80ies and Ian Paice auditioned with The Who and was favored by JAE, but Townshend preferred Kenny Jones as someone he knew from the 60ies (IMHO and not as a DP-fanboy: a mistake from a purely musical view, Jones was wrong in so many ways for The Who). None of the Purple split-off bands ever had the artistic stature or commercial impact of Purple, not even Rainbow (which had the benefit of featuring Purple's main musical driver). With latter day Whitesnake being the exception, but it took Coverdale more than 10 years of hard work from the ground up (Whitesnake's beginnings were commercially humble to say the least) to re-crack the US in a comparable way to heyday Purple.