The nature of our work means that we do actually know most others! It’s a hospital Dept which provides a 24 hour a day service, working a variety of shifts so we work with different colleagues all the time.
But equally, the fact you work with different people from the 100 or so all the time, means that it is unlikely the people are that close to you.
This will be ingrained in the team now so I think any suggestion of stopping it or changing it will not be warmly received!
Or there will be a collective sigh of relief, from everyone else struggling to put a fiver / tenner in an envelope 2 or 3 times a month, for people with whom they only have a passing relationship or who are really only an acquaintance on top of having to go out and buy foods to bring in 2 or 3 times a month.
Various suggestions could be
This 'tea party' can the people whose names begin with A - I all bring something. Next occasion can the people whose names begin with J - R bring something, 3rd time people with names that begin with S - Z. So, less stress of having to bring all the time , less expense of having to bring all the time, and less waste.
For the collection, everyone pays into 'the fund' either set amount, or, if thought fairer, a proportion based on earnings (so Consultants are expected to pay more than porters, and, if people think fair, PT staff pay less than FT staff - but, whatever rules people think fair), either a small standing order each month, or every 6 months or whatever, then the gift is bought out of the fund up to an agreed amount. Seems a bit clinical, but less pressure on everyone. If anyone doesn't want to join the fund, that's fine, but they won't get a gift when they get married / have a baby / have a zero birthday / etc.