It is true that b-trees aren't ideal in that respect, and you will see some amount of write amplification, but not enough that it should be a major consideration, in my experience
You really have to take into account workingset size and cache size to make any judgements there; your b-tree writes should be given by journal/WAL reclaim, which will buffer up updates.
A purely random update workload will kill a conventional b-tree on write amplification - like I mentioned, that's the absolute worst case scenario for a b-tree. But it just doesn't happen in the real world.
For the data I can give you, that would be bcachefs's hybrid b-tree - large btree nodes (256k, typically) which are internally log structured; I would consider it a minor variation on a classical b-tree. The log structuring mean that we can incrementally write only the dirty keys in a node, at the cost of some compaction overhead (drastically less than a conventional LSM).
In actual real world usage, when I've looked at the numbers (not recently, so this may have changed) we're always able to do giant highly efficient b-tree writes - the journal and in-memory cache are batching things up as much as we want - which means write amplification is negligible.