Hi, that's a completely valid concern! I think when applying to those smaller firms, rather than plainly removing the Open Days, I would try to focus on how you frame them. At the end of the day, each one of those experiences perfectly showcases your drive and motivation towards the career. This is alongside teaching you various skills that would be useful. However, at the same time, you're right it may potentially make you seem like a candidate who isn't truly targeting their firm.
As such, I would see if maybe you could rewrite the entry without namedropping each firm. For instance, I wrote: "I have been selected after competitive application processes to Insight Experiences at 10+ top city firms". This is then followed by slightly more detailed insights without directly mentioning where I learnt each thing. As a result, I was able to retain the necessary information that I wanted Graduate Recruitment to see, without any overthinking as to whether the MC recruiter thinks I'm too US heavy (I was haha).
Hopefully this helped

!