Hello,
Is it feasible to build a custom bathtub using the same approach as building a shower ?

Build it like a pool. Just make sure you use the correct thinset, even though the water submersion is only for a short time.

Waterproof with Laticrete 9235 or Schluter Kerdi.

there some differences between pools/bathtubs:
1. Temperature changes : room temp --> about 40 c --> room temp
2. frequent fill/empty cycles
3. a person moving/walking on the structure (where's a pool has a fairly constant load

my worry is that the thinset will crack/develop fissures

However it's built, there would need to be absolute stability ... enough to support the volume of water at 63 lbs per cubic ft plus people.
Expansion and contraction would need to be addressed both with the supporting structure in relation to the tile system and the tile system itself.

Temperature changes are no more an issue with building a tub than it is building a steamroom or sauna bath. It can be done .... but I for one have never attempted any such task and don't feel qualified to advise anyone else.

Well then since I don't fancy 600L of water making a nice waterfall (we live on the 6th floor) I will leave this idea alone...

thanks for the advice