We did not invite “guests” to our wedding. We did not have a large wedding, and preferred that everyone in attendance was someone we already knew or had at least met a few times…
No matter how big your wedding is, of course it is OK to restrict the guest list to people whom the hosts and guests of honor actually know. It takes a bit of chutzpah to imply that a guest has some right to bring a total stranger to an intimate event like a wedding simply because the hosts know a lot of people.
Miss Manners considers it to be a social blunder to put “and guest” on a wedding invitation. If you want to invite someone, you take the trouble to learn their name and you extend an invitation to
that person. Guests with a socially established partner should not be invited without that partner, while guests who do not have a socially established partner are not allowed to ask to bring a guest. Substitutes may not be sent in lieu of invited guests. If multiple people are included on a single invitation, it is still OK for only one to accept the invitation if the others have to send their regrets. Common sense ought to reign, of course: If a person who needs assistance can attend but their spouse cannot, it would be OK to ask hosts if an assistant could come in lieu of the spouse, so that the person needing assistance could attend.
As your example points out, OP, it is not an imposition to suppose that a single person could enjoy attending the wedding of friends or relatives without a date. If the person has a socially established partner, the couple ought to be treated as a social unit. Otherwise, it ought to be assumed that an adult is perfectly capable of socializing in a group of friendly adults without having to bring a social ally.
If someone RSVPs and presumes to include someone not on the guest list, the host ought to find out if this is someone in an established relationship of which they were not aware. (Someone invited alone as if he or she did not have a partner is allowed by etiquette to ask that the host invite their partner., and many hosts would pray that they will!) If a partner has been left off by mistake, invite the person and apologize for the oversight. If that’s not the situation, the faux pas of the guest doesn’t have to be overlooked. It is within the host’s rights to remind the person that the guest list was carefully chosen, that some persons that might have been invited had to be left off of it, and unfortunately the host won’t be able to include the guest who has been “proposed.” (It is not necessary to beg limited financial resources or a limited venue size. A wealthy couple does not have to invite the entire planet to their wedding just because they “can afford it.” It would take a seriously offensive amount of chutzpah to suggest otherwise.)