Is there any reason to stop transaction log backups during a maintenance window?
You are absolutely correct. There is no reason to stop Transaction log backup during index maintenance window. It will only make things worse as you already experienced.  I had cases where I was doing maintenance on smaller size indexes I even took transaction log backup more frequently than my regular schedule.

In case if you are rebuilding large indexes you need to make sure that you have enough storage for transaction log to grow. Even you take transaction log backup during index rebuild logs will not be truncated when you have a long and active transaction.  That is not the case when you reorganize indexes because logs can be truncated in between while reorganizing a single index.

Even in the Frequently Asked Questions page of Ola Hallengren this is mentioned:

The transaction log is growing very large when I run the IndexOptimize job. What should I do?


  Make sure that the transaction log backup job is running as it should.
  
  Check that the transaction log has the storage that it needs. You
  should not shrink the transaction log file. Doing so costs resources
  to shrink and later to regrow the file.


During full backup there is no need to stop transaction log backup.  Read this article by By Erik Darling.

What happens to transaction log backups during full backups?