Hence - you could not fill a bath from one tank
That's a choice. We chose to keep roughly the same size tank as the oil system used, which fills a bath and a bit, but the extra insulation on a modern tank meant it had to be relocated to the loft, which is possible now because of the extra insulation... this had benefits that the back of the airing cupboard was used for some of the ASHP equipment and then boxed in (with removable panels for servicing, and using the old backup immersion heater power feed), and the pipe run from the tank to some hot taps is shorter than before.
PLUS - as soon as you start running a bath then the tank start topping itself up with water - which is obviously cold
Hence the hot water you are using become cooler.
So if you are in the bath - and it is getting cold - then if you try to top it up with hot - it comes out as luke warm
Again, that's a choice. Ours draws the hot water from the top of the tank while cold is added to the bottom. Eventually it will homogenise to be colder and then be reheated, but not in the time it takes to have even a long bath. Also, when the reheat kicks in, it heats the bottom (cold) part of the tank and heat rises, so it doesn't stay lukewarm long. Of course, it is possible to end up with lukewarm tap water if the settings are wrong, but it's not inevitable unless you try running two very full baths inside an hour. There are also a couple of thermometers in the tank and a display by the bathroom door, so you at least have some warning that pressing "force reheat" and waiting a few minutes might be a good idea, which we never had with the old tank.
and the heat pump does not have the thermal welly of a gas boiler and so will warm it up much slower
Slower, but the extra insulation on a modern tank means it isn't that much slower. It is true that it can't lift the temperature from cold mains water to hot tap in one go like a combi boiler does, but those tend to be horribly inefficient at either water or heating or both. You can't design the same heater to do both temperatures well.
same would apply for a shower - I presume - if two people had one back to back and took their time
It's less of a problem with a shower because you (or the mixer control, if thermostatic) tend to react to the gradually reducing temperature by changing the balance of hot and cold.
On top of which there is the "needing bigger radiators" problem
plus we have no idea how good the insulation is here but there are horror stories about the builders and insulation - from people who have lived her a very long time
so we won;t be heading in that direction without written guarantees
If I'd done something different, it would have been to have an insulation surveyor check the insulation first with cameras and not trust the old-fashioned surveys, even though Ofgem trust the pathetic EPCs for grants. Some will check it for free, in the hope that you'll buy from them if an upgrade is needed or possible. The one who checked ours was great but they didn't sell the insulation type we needed (due to restricted access for installation). So we got Aran Group from Suffolk in, who also seem great.
I think some suppliers do now offer guarantees, including Octopus and Heat Geeks, but so far they are either pretty conservative about where they'll install (so horror stories about builders might deter them) or charge quite a bit extra to fund the stronger guarantee. I think you also surrender some control over the installed system settings, else the guarantee is voided, but that's probably OK for most people who don't want to innovate much with their heating.