Why doesn’t a MySQL fulltext search “IN BOOLEAN MODE” fail when referencing a missing column?
This is documented behaviour:

InnoDB tables require a FULLTEXT index on all columns of the MATCH() expression to perform boolean queries. Boolean queries against a MyISAM search index can work even without a FULLTEXT index, although a search executed in this fashion would be quite slow.

Why this exception exists (which is what you are asking in a comment) is speculation and something to be answered by the original developers, but there is something that you cannot do without this exception:
a boolean search that spans multiple tables.
For a natural search, you could compensate with or over separate matches (one for each table), for a boolean search, it would fall into the range of &quot;much harder&quot; to &quot;impossible&quot;, which could explain the asymmetry.
If that was added as a nice feature to the (MyISAM) boolean search, and at least one user relied on it, you can make an argument for not removing it, as the only disadvantage of not forcing an index is that it could be slow if you make the mistake of forgetting the index (which can and will happen with normal indexes too, see 90% of SQL performance questions on Stack Overflow).
MySQL is really not in the business of protecting users from themselves, see e.g. only_full_group_by=0 (that can give you unintended results if you are not careful) or grant (that, before MySQL 8.0, could create a new user without a password if you are not careful).