Actually, I had written an almost complete response to your multi-feature request from last night, but then I fell asleep just before I finished it. When I woke up and looked at this thread and all the replies that had been posted in the meantime, I wanted to incorporate them, but when you suddenly completely rewrote your opening post, I extracted the one part that hadn’t been seen here before and am now posting only this fragment taken out of context:
That Toolbox customisation thing can already be covered, at least in part, by the Workflow Buttons plugin.¹ In part because I currently don’t know if it allows adding single brush presets, I don’t think it can, but I may be wrong. So it may be already existing, but it can also be that it would have to be extended. Let us assume the latter.
That is not wrong, but all these approaches to create an eraser tool that behaves like that from PS are kicking the users in the back who love the Krita eraser. So, for me, the only acceptable way would be to have that optional. Why? Because I hope that this constant nagging about Krita’s eraser will stop then and doesn’t steal “my Krita eraser”, because I don’t want to see it being sacrificed for an eraser I dislike.²
Michelist
¹ I do not know if you have noticed or tested it so far, but Krita now allows you to build your own Toolbox using the Workflow Buttons plugin, which is a Krita stock feature, so it is nothing you have to install, it already ships with Krita:
² I cannot understand that people can switch cars, phones, TV sets, or stereos without nagging their manufacturers to rebuild their products because the users former manufacturer made this or that different, but when it comes to Krita, then it has to adapt to other software to maybe make users feel comfortable who only want to have a free PS clone and are by no means willing and able to adapt to Krita.
And I’m sure this never-ending nagging can only exist for one or two reasons.
Reason one: Krita seems to have so many advantages over PS when it comes to painting that they would like to have and use Krita, but no one ever stood up and paid a developer to implement this oh-so-important thing so it can be merged into Krita and make that part of the artist’s world who wants that smile again. Hopefully that ends this discussion once and for all.
Although, why isn’t anyone pestering Adobe, Celsys, and whoever else out there to make their eraser work the same way as Krita’s? 
Then, in the future, no one will have to worry about how Krita’s eraser works… 
…they’ll know it. 
Probably those companies will show you the finger.
Reason two for some will most likely be the money they have to constantly feed into the pockets of these corporations.
I think that if everyone who has spoken up for this eraser tool here and elsewhere - which seems so indispensable to these artists - had chipped in between €50 and €100 (or even just the annual fee they have to pay to the proprietary software companies they apparently hate to support so they can break away from them and switch to Krita and save their money) instead of continuing to throw money down the throats of Adobe, Celsys, and the like, then this feature could have been programmed a long time ago.