Marketing: why don't venues promote events happening at their venue even if organised by a third party?

Summary: venues run their own events and also hire space for others to run events. While venues will promote their own events they don't seem to do much promotion for third-party events, why?

As an event-goer my main reasons for wanting to go to an event are that I like the work of the performer(s) or am friends or colleagues with them, that the event sounds interesting even if I don't know anyone involved, that I simply want to go and see an interesting or as yet unvisited venue (that's a reason isn't it?!) or that I've been cheerfully dragged along by a friend.

I rarely give much thought to who the promoter of the event is but apparently this factor can make a big difference to how a venue advertises or promotes an event happening there. Learning this has surprised me a lot and I'm not sure I can really make sense of it, to the point where I think that my perspective must be missing something and perhaps I'm just wrong (if you know, tell me).

Clearly the event promoter can pay for newspaper advertising as that shouldn't fall to the venue but I'm mostly talking about social media (Twitter / Facebook) and email. Things that cost time and effort rather than money.

When I'm at an event I don't know if it's been produced by the venue itself or an outside promoter and don't really care that much about the difference between the two which, for the purposes of event-attending, is irrelevant.

Here's why I think venues should also tweet or blog or post to Facebook about any event that's taking place on their premises, even if they're not the ones producing or promoting it.

a) Offer event-advertising as a perk to the event organiser 
"For a [£ reasonable fee] we'll promote your concert for you" - seems like an easy enough thing to upsell if a venue has lots of Twitter followers or Facebook people. A discussion could be had about the timing, content and frequency of tweets (10 am on a Tuesday morning might reach more people than 7pm on a Friday night etc). Or a budget option might be retweeting one or two tweets that mention the event and the venue.

Caveat 1: there can be a bit of red tape in sending a tweet or Facebook post particularly if you have more than one person managing the account. Some organisations have different sign-off procedures but I can't see very many problems with retweeting a simple "this event is happening at this venue" tweet or liking a Facebook post that someone's tagged the venue with.

Caveat 2: to ensure fairness in terms of not tweeting loads about one event to the exclusion of another it's very very simple to search from:CoolVenue EventName to see how many tweets have previously been sent about it. This does take a bit of extra work. But not very much.

Obviously this has to be balanced for a large venue that has a lot of events, otherwise followers will just be swamped by information. One way round this might be to send out a tweet with a picture that shows several events at once, and a link going to a page where the individual events are linked. Incidentally the BFI are were* very good at this and create a tweeted picture with all the films they're showing that day.

*I think they stopped during Covid and didn't restart

b) It might get more people in your venue, eating your food, seeing your flyers
Presumably the more people you get into your venue for any event the more likely they are to see your flyers for your future events, or eat your food and drink while they're there. 

c) Helping your audience to experience your venue at its best
Perhaps having more people present increases audience enjoyment slightly as they get to see a whole load of other people filling up your venue and having a good time. More people in the audience could also mean more audience tweeting and instagramming about how great the event and venue are, which you can then show off to people as evidence of awesomeness.

Bonus: all marketing emails should include subscribing information
This isn't that intuitive because if someone receives your email they've subscribed already but I often forward emails to friends so I think it's a good idea to include subscribing, just in case, not just how to unsubscribe.

Perhaps this is all too difficult
Given that the things suggested above aren't routinely done... is it because I've underestimated how much effort is involved in putting on events? All my events are fairly small - 20-100 people, pretty easy - or are there other good reasons why this isn't done very much? Or is it done loads and I'm failing to spot it?!