I think it's extremely misguided to say this is a queue jumping system. It seems there have been s couple of glitches that have been resolved now and it is only people already eligible for the vaccine that can book in.
When people do book in themselves they are are saving the NHS the huge administrative and logistical burden and thousands of man-hours (person-hours!) of trying to contact every single presently eligible person, and helping the process of getting this country closer to functioning again.
I can not see how the system would crash, any more than the self assessment system crashes when millions of people file online at the same time in the last days of January. It's not the 1990s, these systems are designed to cope with huge numbers using simultaneously.
The loo roll parallel is a really not accurate...nobody is stockpiling 100 vaccines for themselves, they are simply able to book for their one when they are eligible. It's more like a supermarket being desperate to get a single loo roll out to everyone who should have one before they have to chuck them away, and being relieved when people take the steps themselves to come in to collect their loo roll as they don't have enough staff or man hours available to personally contact every single one in a timely manner. They would rather the loo rolls get to those who need one, rather than sitting uselessly on the shelves out of a misguided notion that for someone to have one, when it is rightfully theirs, is somehow queue jumping.