Since you like analogies it's like me having a washing machine that doesn't get my clothes clean. I complain and the manufacturer says well it's your fault for having dirty clothes, if you didn't get dirty then the washing machine wouldn't struggle to get your clothes clean.
I do like a good analogy, the more bizarre and humorous the better, although there's limited scope for that here.
So picking on the washing machine analogy:
It's more like you inherited a twintub from your grandparents, who found it to be perfectly functional for getting their lightly soiled clothes clean, and you also found it to be fine for that purpose.
But then suddenly got voluntold to wash 5 rugby teams worth of muddy kit and found it just didn't cut the mustard, took forever and constantly looked like it was on the verge of packing up.
It's not the fault of the machine, or of your grandparents who gave you it, nor is it your fault because you didn't set out to be in the situation...
But you're still faced with spending a long time trying to baby the machine through all that muddy kit one way or the other, before you can sort out an alternative arrangement.
If I need to pay more tax to get the NHS working properly then fine, I will do that, but I want it done properly, not just throwing money at highly paid bureaucrats to fiddle the figures and then when the system starts to break down we are told it's our fault for getting sick.
Now, taking that as a general point I can fully agree with you on that!
In general I'm not overly fussed by paying tax, but I'm deeply miffed when it's obvious that the money we all put in is not being used wisely.
However in the wider context of your remarks, around lockdowns, etc, I feel that my point stands; the fact that we're both angry about mismanagement of taxpayer funded public services leading us to a situation where one of the ones we all rely on doesn't have the resources to deal with a foreseeable natural disaster, doesn't absolve us of the responsibility to do (or rather not do) what we can to help the wider community.
Continuing the analogies, the argument that because you pay tax, and the NHS is still underfunded and if it wasn't we shouldn't need a lockdown...
Is similar to standing in a burning building, arguing that because you've paid fuel duty, and the building shouldn't be on fire, it's perfectly reasonable to expect you can pour petrol into jam-jars at this very instant.
In normal circumstances it is a perfectly reasonable expectation, but the context of the specific situation absolutely matters, even if the situation shouldn't ever have arisen.
Taking one such point in particular...
I don't think so, not when I am paying for something that isn't fit for purpose through no fault of my own.
I'm not sure if you're one for poetry, but this counterpoints your sentiment quite well:
No man is an island entire of itself,
Every man is a piece of the continent,
A part of the main.
If a clod be washed away by the sea,
Europe is the less,
As well as if a promontory were,
As well as any manor of thy friend's,
Or of thine own were.
Any man's death diminishes me,
Because I am involved in mankind.
And therefore never send to know for whom the bell tolls
It tolls for thee.
— John Donne, Devotions Upon Emergent Occasions and Seuerall Steps in my Sicknes - Meditation XVII, 1624