I reproduced this behavior in PostgreSQL 10.3 with a simple bash loop and a two-column table, one of which is fixed and the other is repeatedly dropped and re-created until the 1600 limit is reached.
To me this is pretty cool, since I can use this limit as leverage to push the developers to the right path, but should Postgres be doing that? It's as if it doesn't decrement some counter when a column is dropped.
This is working as expected. When dropping a column, or adding a new column that can contain nulls, PostgreSQL does not, and does not want to, rewrite the physically stored records/table. Thus it must be capable of accepting records formed for prior table versions which means it must keep track of those now-deleted columns.
I'm sure that there is more to it that requires reading, and understanding, the source code to comprehend; but that does seem to explain why its works the way it does.