We've done way more than 11 , but that's across three DC! For DC2 and 3 there was at least some memory of those we saw the first time around.
If you've got enough time, OP, you'll find you can fit in quite a few in 'drive bys' for first impressions. For instance, Nottingham is just off the M1 on the way to anywhere; go to York on the way to Durham; see Warwick on the way to Birmingham. You can do Cardiff and Bristol in one day. That kind of thing.
And if London is involved, you can fit in two proper open days at once ( if they're scheduled at the same time) - or one open day and one drop in.
In answer to the question, are they useful for parents? For me, yes, always. It depends how involved you are or want to be in his decisions and about half of people on here will say "it's all up to him' and the other half will say ' I've helped him make every big life decision so far, so of course I'll be involved in this one'.
For us, once you've got passed the course content and the entry requirements and is that the right 'fit' for you, much of the rest of it is on 'feel' so actually going with him is very helpful.