What happens when full backup, differential backup and log backup schedules collide

There are quite a few solutions to have your daily backups (full, diff and logs). You could:

• Write your own script: it might be useful if you need a fine control on it, or if you need to respect some naming convention. I did not test it, but your code looks reasonnable.
• Use the maintenance plans: very easy to set up, but less control. This might be a good solution in your case.
• Use a 3rd party script / tool: Ola Hallengren's scripts are very good, but you can find plenty of others.

There are multiple ways to get to the intended target recovery point with your setup.

A few things:

1. You cannot eliminate log backups for the most important reason of transaction log re-use.
2. It's not possible to know when an issue will occur and thus having multiple ways to get to the RPO is useful and sometimes necessary.
3. Differentials aren't a substitute for log backups, they will lower the RTO as they are much faster to apply than log backups but ultimately aren't worth much on their own (spanning broken lsn points, etc, is useful)
4. How are you going to know which ones you need and don't need ahead of time?

I would not stop taking log backups but you could put into place an aging mechanism in your backup software or process to eliminate files that are no longer needed.

Using your example, you have many paths but the basis is as such:

Always take a tail of the log backup first

1. Restore the full backup, latest differential, all logs.
2. Restore the full backup, all transaction logs.

This is more flexible as a corrupt backup file (say a log file) could be spanned by a differential or a corrupt full could be spanned by differentials, etc.

I would not change how your strategy is currently, but I would make sure it meets your RPO and RTO requirements.