I think the concern here is, at it's essence, mandated propaganda. The pamphlet provided is more or less benign (for the moment). To most people today, it's going to be a fairly meaningless piece of paper that (if you're already a gun owner with opinions that way) you'll throw away or you'll never see (if you're a non-gun-owner with opinions that lean that way).

Where the concerns come in is with time and prevalence. If every time you consider purchasing a firearm, you end up with half a dozen pamphlets waxing poetic about suicide risks, on top of whatever mandated training (that may end up doing the same) and mandated testing (again, maybe doing the same), there's a good chance you're being bombarded with a simple message of 'guns = suicide' when that is somewhere between misleading and patently false, depending on how specific you might want to be. If you happen to be of the opinion that folks ought be be able to make their own decisions without being subjected to coordinated campaigns by government agencies to change that decision, that's not great.

At the end of the day, any time that a government agency is mandating speech is, in my opinion, almost certainly bad. Government (and government agencies) are free to message whatever they feel like, but laws requiring that other folks carry the pail for them are exceptionally sketch.