There may be enough toilet paper somewhere but it's not where people want it: on the shelves.

People aren't rational actors, and by saying "they don't really need toilet paper", you're not solving the issue that is people seeing empty shelves for toilet paper, bread and soap and thinking that the system is failing.

You don't want the public to become nervous, ever. Nervous people make terrible decisions. And for a government to look uncaring/impotent is the way to make the population nervous.

It doesn't really make sense to increase toilet paper production though. There's no long-term increased demand, so the problem will probably sort itself out in a couple of weeks once everybody who has been panic buying already has a stockpile.

The trust damage will be done by then. It's like a stock market crash because of some irrational behavior. Sure, "it'll sort itself out in a few months", but you'll have companies going under, mass layoffs etc by then.

Also, I don't know whether they'd actually need to increase production. According to super market chains, they have more than enough but it's in their storage centers and they have issues/aren't prioritizing getting it into the stores.

Exactly, it's akin to a run on a bank - if all account holders of any bank withdraw all their money at once - NO bank would cope with that. Though a run on toilet paper just hit the supply chain, so you get these bumps. Come mid to end of summer, there will be a surplus of toilet paper due to the run of panic buyers fueling panic buyers all over-stocked.