dnd 5e – Is this recommendation for a fighter to take the Weapon Master feat entirely useless?

In short…

Yep, complete waste of a feat. There are no core weapons that a Fighter can’t use.

Covering the Bases…

There is a precedent in the DMG for having weapons that PCs do not have proficiency for, such as Firearms

It’s up to you to decide whether a character has proficiency with a firearm. Characters in most D&D worlds wouldn’t have such proficiency. During their downtime, characters can use the training rules in the Player’s Handbook to acquire proficiency, assuming that they have enough ammunition to keep the weapons working while mastering their use.

The Pincer Staff used by Kuo-toa and a Fighting Chain used by a Chain Devil are two examples of weapons that exist in the world of D&D, but are not listed as Simple or Martial weapons. But this is firmly in the realm of DM’s Call as to whether or not a Player Character would be proficient with such a weapon.

Additionally, it is possible to gain proficiency in Improvised Weapons (which are neither Simple nor Martial) by way of the Tavern Brawler feat

However

You gain proficiency with four weapons of your choice. Each one must be a simple or a martial weapon.

This line was the subject of errata which added the bolded clause. So you can’t use this feat to gain access to ‘Exotic’ weapons of any sort or Improvised Weapons.

Thus, in all cases, the Weapons Master feat is useless to Fighters. It grants proficiency in Simple or Martial Weapons, and you are already proficient in all Simple and Martial Weapons