Everyone? Really? EVERYONE?
So, better coverage than voice is in current humans?
ie: no Deaf, no mutes?
If you have mental disabilities (ie: can't broadcast/can't receive), then those people will get/develop language (probably, assuming they aren't killed as subhuman animals (or demons); if other people can't detect that they have thoughts). Primates vocalize, and can learn sign. No reason that your disabled wouldn't at least get a grunt code. They might not get fluent, verbal language going, as there's no great evolutionary advantage to mutants with better vocal range - if most people are using telepathy.
Basically, you're going to have some problems in getting your primates vocal language, if there's no evolutionary need for it. We speak more fluently than primates, because there was a decided evolutionary advantage to mutants who had better vocal range/abilities. If you evolve the telepathy in parallel with language, it would get you the capability to speak (roughly; retraining people to speak, even though they have the vocal cords is time-consuming and difficult). And telepathy would definitely trump language in use.
However, the confusion that language engenders - miscomprehensions, etc. have led to a number of discoveries, because people thought someone said/meant something, when they didn't. And so people started investigating things and trying to find solutions, because they 'knew' someone had already done that.
Without vocal language, I don't see how you're going to get written language. Most alphabets were codes for phonemes. How do you make a sign for a thought-complex? Especially if telepathy is faster/more complete than language. Might be easier to train your memory and download/upload all of the history of thought on a subject to your pupils... who'd then memorize it, and could give it immediately to their pupils... I can see that there wouldn't be any schools :)
Is there any way to shield your brain, to keep secrets/lie, and to have spies? I can see languages developing if you want to keep who you are secret from your recipient: both go into adjacent booths, and use the Police language to do anonymous reporting.
Okay, language is getting a lot of comments. (and I was hasty to slight Chinese/pictograms by giving them the short end of 'most' - but yes, I did give them a moment's thought; however they had and failed at printing because of their inherent disadvantage, and only committed to printing when they knew they had to catch up or be in the dustbin of history. Not a recommended technology.).
But, let's keep in mind the question. If you can transmit an actual picture into another person's brain... why would you try making art to eventually derive a simplified script from?
Granted, if people have poor memories (and I think if we had evolved telepathy, we would've selected for photographic memory as well) they might want help/memory aids. But, I suspect that it would be a much more mind-based history. We had oral-history for long, long periods in our history - I think that would be magnified many times over with telepathy.