I've almost never had a problem big pulling in instances and this was my first MMO I've even played a tank extensively. The cooldowns are very straightforward and your AOE DPS rotations on tanks are...1-2 buttons like everyone else. Not everyone learns at the same pace, but that's why the Trusts exist for dungeons now. You learn your job until you're comfortable and take it to the "big leagues" (honestly the 4mans are a snooze fest without big pulls once you get to know them).
That said, while EXTREMELY rare, I've had healers who were uncomfortable with big pulls who I just slow down for, no biggie. But if you don't ask me to straight off I'm starting that instance at mach speed, as that is the usual preference of everyone involved. This has only bitten me in the ass once that I can recall, where I started mass pulling in Akademia Anyder and the healer just.../quit about midway through the pull. No red line of D/C, no "g2g sorry", just an instant disconnect and "Replenish Ranks?" message.

Not sure what that dude's problem was but it does touch on a point most people seem to be glossing over here: Big pulls are the default play, dungeons are designed with hard "walls" with this in mind. Now you can go beyond this in places like Mt. Gulg where you can make pulls I wouldn't trust random healers with, because it's 5 massive piles of mobs, but for the most part, you should be able to handle 3 packs of mobs in nearly any dungeon with ease. Tanks are designed for this, their cooldowns are balanced perfectly around being able to do this. If you DON'T do this, half of your skills as a tank are sitting there uselessly. There's nothing wrong with playing sub-optimally, but you have to accept that you are de facto choosing to inconvenience someone for your own benefit. There's especially nothing wrong with telling people "Hey I'm learning and not quite there yet" although one starts to raise eyebrows by the time people are in 70+ dungeons.

The true tactic here is to just play PLD when you tank. As soon as you get Clemency your healer is almost entirely optional in any 4 man content. With two competent DPS you LITERALLY don't need one.