You're right in general terms. The statistics for most of Europe suggest that with the current case rate postponing vaccines even by a few days, will lead to more deaths than the possible deaths observed due to adverse reactions.
But ethically and morally, when you give vaccines to healthy people, especially those who have a low personal risk from the disease, you have to set your standards higher. The ones who die from an adverse reaction are not necessarily people who were going to die from covid.
The holds arise from small numbers of unusual cases appearing in a short period. With incidents being monitored more carefully than normal, odd coincidences can happen. Equally though, something real may be happening.
If it turns out that a production batch, or the distribution and dispensing system was faulty in some way, then the lessons could be important globally. If we can find out more about the people affected, then we might discover something that allows us to predict adverse reactions and steer some people to a different vaccine or no vaccine.
Lots of people are vulnerable to blood clots and to platelet damage, and it clearly doesn't affect all of them - else the UK would have seen it. If it turns out that the effect gets magnified if you're low on vitamin B12, take the contraceptive pill and gets migraines, or something equally random, then it becomes the starting point for discovering a whole lot more about the vaccines and beyond.