A problem that comes up from time to time when I am talking to priests is that of jinja capacity.
Suppose someone wants a gokitō (a personal matsuri making a request) performed. This must be done by a priest, so you need to have a priest there. If the only priest at your jinja is not full time (as is the case for most priests), this presents an immediate problem.
If you do have a full time priest, for example because the chief priest’s mother is retired and has a license, then you can do it, with a bit of notice. You can even do two groups in a day.
If thirty families turn up wanting Shichigosan on the same day, however, there is a problem. Doing them one family at a time would, realistically, take at least ten hours. (A gokitō itself can be done in ten minutes, but you also need to get people in and out of the prayer hall.) Of course, you only have one priest. So that priest gets no breaks all day.
That, obviously, is not practical, so you have to ask families to combine their ceremonies. This can get quite extreme. At the most popular jinja for gokitō (apparently this is Samukawa Jinja in Kanagawa Prefecture), I am told that they have at least four priests at every gokitō. One performs the matsuri, and reads most of the norito. The other three kneel behind him and simultaneously read through different lists of names of people who have requested gokitō (not all of whom are present), so that all the names can be read during the matsuri.
One might feel that this lacks the personal touch, but the alternative is to turn people away. Of course, jinja that simply do not have enough priests have no choice — if there is no-one to perform the ceremony, you cannot have a gokitō.
It is also difficult to respond if a jinja starts getting more requests for gokitō. You need a lot of requests to pay for an additional priest, and you also need to have confidence that the requests are going to continue. There simply isn’t a pool of Shinto priests available for casual employment on zero-hours contracts.
Jinja can also have problems with too many people visiting for goshuin (the red stamps issued to show that you have paid your respects at a jinja) or omamori. On the first day of the Reiwa era, so many people wanted to get a goshuin from Tokyo Daijingū (a jinja famous for enmusubi — good relationships) that the queue stretched out of the jinja, down the street, round the corner, onto the next street, and so far that the police came and asked the jinja to stop, because the people queueing were interfering with traffic.
That is, obviously, an extreme and special case, but jinja can get so popular that it is difficult to respond to all the requests for omamori. At least, in that case, it is possible to hire local students to work as miko on a short-term basis, but there is still the issue of the physical size of the jinja.
Popularity, even the right kind of popularity, comes with its own problems.