I also work for a University in a niche field and do my best to accommodate requests, but I get more students than I can manage, and honestly it's really hard work! They can't be left alone, everyone involved needs safeguarding training, lots of paperwork to be filled out etc. So I now do two structured sessions a year, and once they're full that's it.
If a student sent me a CV I'd be unlikely to read through it - they are always like the type of thing you used to put in your Record of Achievement back in the day and I just don't have time to go through them. However, I do think that finding their own placement is important - that's the reality of getting a job, it's not always easy and rejection and no responses are common in the real world of employment.
A short to the point email about why they feel a work placement in my field is relevant to them e.g. I'm hoping to come to your uni and study this, my relevant hobbies to the field etc will always make me more likely to consider them (and I do reply to all, even if we can't take them).
Two red flags for me:
They aren't really interested in a career in my field, just looking for a generic placement or because its handy;
When their parent writes the request for them (this puts me off massively because it suggests a real lack of interest/confidence from the child, even if that's not the case, and typically I find these children much harder to engage when they come).
I'll always accommodate someone who has a genuine interest, so I'd suggest having a good think about what the child might want to do and being very targeted in who they approach. There are also organisations who can help. I'm in a science field so e.g. https://www.stem.org.uk/placements and https://www.nuffieldfoundation.org/students-teachers/nuffield-research-placements can help too.