Two of the Definitions of Treat as found both in Miriam Webster and Oxford Dictionaries
a: to provide with free food, drink, or entertainment 

b: to provide with enjoyment or gratification.

There are many definitions of the word “treat” including to pay for someone’s meal or to treat a patient, to treat a person badly or well.

When working with dogs, it’s my belief most people have hesitation or objection to using food as it’s immediately thought of as definition b: to provide with enjoyment or gratification.

It seems frivolous. It’s associated with special occasions not with something essential.

A reinforcer is something that increases the likelihood that a specific behaviour or response will occur. We use food in dog training to reinforce desired behaviour. We also use access to play, sniffing on walks and belly rubs, to name a few.
As long as whatever you choose increases the likelihood of behaviour occurring again it's a reinforcer.

In my opinion, if more people thought of food as a reinforcer there would be less objection.