If you didn't care how fast the instance or non-instanced outdoor "dungeon" was progressing (and you had to manage a certain speed, or you'd eventually get swamped by respawns, when that was still a thing), you could do it as long as the group could balance aggro (and/or kite, when that was also still a thing), with damage and healing. We did some really wacky group compositions back then, because that was what we had. And the old talent-trees encouraged it, as a shaman or paladin or druid (or even warrior) could take some talents to let them tank better, while still keeping their character viable for solo-questing or as a dps. And the game and other players didn't actively punish you for being sub-optimal. (I.e. you could, to an extent, successfully aim for breadth instead of depth, because other players were more accepting of the trade-offs involved, for a variety of social and practical reasons.)
I leveled my pally back in the day as a holy/prot hybrid pretty much exclusively via group questing and dungeon runs. Having decent gear for both roles and understanding the abilities was even more important than talent choice, although good talent choice helped. I remember a great deal of my healing set was leather or cloth, because that's what had the best stats for it, which in turn made it problematic to switch roles mid-fight. I suspect that today, even if I could re-build the character as a working hybrid, it would be an unpopular choice because I wouldn't be as fast as a specialist. But "In the Good Old Days" success and good play still mattered.
Much of that is dead now, unless you are in or can join a community that preexists.
I remember using my bear in WoW to tank as a hunter because we got bored waiting for a tank to become available and one of the dps suggested we try because getting another dps was easy and it was better than sitting around stormwind.