I grew up in a grade 2* house. It's absolutely gorgeous, and so special, but it put me off ever buying a listed house. I live in a 200YO house now (not listed), and even some of the challenges we face with this annoy me compared to something more modern (although I guess not enough to have put me off!!).
Things that drive me crazy about my parents' house (and some of this is unique to a grade 2* rather than grade 2):
-plumbing is shocking - terrible water pressure, showers aren't great. Takes forever for the downstairs loo and kitchen hot water to warm up, thereby wasting tonnes of the stuff.
-electricity - I suspect you'll need a rewire looking at their setup. Which will require re-plastering. Which will require special materials.
-insurance is crazy high and difficult to obtain (this will be in part due to theirs being thatched). Rules around fireplaces have changed several times over the years.
-EVERYTHING having to be approved by English Heritage - even the garden. It takes forever, and often doesn't seem to make any sense.
-low ceilings. I can live with this TBF, you soon get used to it, but my poor 6'5" husband 😂
-small windows = dark rooms. All the time.
-there is no such thing as a simple job - I suspect this may be partly why so many jobs in these houses look like DIY jobs - it just ends up opening a can of very expensive worms that require specialist skills and materials to do. Once you unpick one thing, it tends to unravel many other issues.