Instead of giving visitors visa free access who hold strong passports, rather make them require a visa prior to entry (meaning they can’t just pack their bags and go, now having to pre-plan in advance and line up for getting a visa & paying money for it, they’re not alone since hundreds more are doing the same thing. There’s also the guarantee whether they’ll be eligible or get rejected on the spot).
It may cause strain on visa applications that’ll lead to mass rejections due to overload. If I were a country that’s suffering over tourism, just rescind visa free access for ALL nationalities (including those who have strong passports like US, UK, DE, FR, AU or CA to name a few) as in when they check visa requirements: it’ll be rewritten as “visa required” rather than “visa not required” prior to entry.
Or, they can apply for a tourist visa many times as they’d like but reject them. (Basically a real life travel “shadow ban” if that’s the right way to say it), leads to them giving up as they’ll know a visa will never be guaranteed regardless of numerous attempts. However, would this move alone reduce over tourism? Since you can’t just show up in someone else’s nation uninvited (illegal immigration).
It curbs international tourism, which can help with over tourism. However, it happens at the national or EU level, which makes the impacts of the border restriction far more reaching than other policies.
It also doesn’t help if there is a large domestic tourism industry. An EU tourism visa could help filter out some American and British travelers, but you’d still have the Schengen Area tourists to deal with.