What would the world be like if we were all alike?
So, here are the downsides to everybody starting out with the same playbook. I'm talking, like, the exact same playbook, you don't go out on the internet looking for eight different playbooks who are all melee-focused fighters and offer a choice.
The same baseline capabilities. One of your stock moves as a GM is to offer an opportunity that fits a class's abilities, as a way to direct the action toward one particular person who might not have had the chance to do much for a while. If everybody has the same playbook that's not really possible, and whoever jumps at the prompt first will have just as much reason to latch onto it.
A broadly similar equipment loadout. Similarly, you've got use up their resources and show a downside to their equipment, but your playbook also determines your starting gear. So their resource pool is either going to be shallow as a puddle or deep as an ocean, depending on what part of it you're trying to hit, and if you show a downside to a piece of equipment that everybody has you've similarly locked everybody out.
Startlingly similar histories. Bonds outline your character's past, both through your own eyes and through everyone else's. But with the same bond slots to fill, everybody's past seems like a weird, distorted echo of everyone else. Oh, Fightgar and Fightgar-1 both think the other one is soft and needs toughening up, how amusing! ...and Fightgar-B and Fightgar-Omega both think the other one is soft and needs toughening up, that's, uh...
Identical or opposite motivations. And when you pick your alignment, well, there's only a handful of options there as well. Either you want to accomplish very different things to satisfy your alignment or you're all motivated to do entirely the same things.
Alternatives to One Starting Playbook
Aside from "grab random thematically coherent playbooks from the Internet", I mean. Both these alternatives begin with starting at level 2, rather than level 1, which isn't that big an ask for a given playerbase, I hope.
Start at level 2 and multiclass. So one person can maybe start out a Fighter, and at level 2 everybody takes Signature Weapon as a multiclass move, even if it wouldn't be an option for their playbook. That weapon is your weapon as a sworn Knight of the Iron Rose, or whatever. (Or, you know, Cast a Spell for a wizard college, Shapeshifter for a druid conclave, etc.)
Start a Compendium Class at level 2. A bit bigger of an ask on your part, since you'll have to build this fictional organization out as its own playbook-esque thing with variant moves and a baseline capability, but on the other hand, well, you're not limited to assuming this organization concerns itself specifically with the starting scenarios for some existing playbook. If the important part of being in a wizard's college is the office politics and the undergrads offering a mix of dangers and opportunities, then you can put all those in your compendium class, the Wizard, Cleric, and Bard are all running their own departments, and the Fighter is running campus security or the events staff.