I'm sure some of the longer preserved lines could host an HST, ie the NYMR or the West Somerset etc etc. I'm not sure, however if they will need purpose built facilites or if the power cars will be equally at home served in a preservation sites loco shed.
I'd love to see at least one FULL HST set preserved. In fact, as one of the most successful designs ever, I would suggest that it should be a priority for the National Collection.
However, please consider some practicalities:
1. Most of the well established lines are chock full of rolling stock as it is. The "full" signs are out.
2. Amongst those lines, the priority is steam, because that is what puts the bums on seats, ie joe public with no interest in railways. If that was going to change, it would have already, as you need to be in your 50s to have any meaningful memories of steam in BR service.
3. Loop length. You will struggle with a 9 vehicle train at many lines.
4. From what I understand about them, Mk III coaches really need to be kept electrically live. MTU engines don't like being cold started. The more modern the traction gets, the more "issues" like this you will have to face. Electronics don't like being left out in the cold and rain!
5. Skills - the lines do not have the skills base for this type of traction.