Okay, let's go over that.

Gloves are used to protect the patient with sterile technique. Before gloves, Semmelweiss and Pasteur taught to wash hands in freshly boiled water for similar reasons. As long as your skin isn't broken, it's a very effective barrier against bacteria and viruses. So we are trying (a) not to get infected ourselves, and (b) not to spread the virus to others if we are infected.

As Semmelweiss and Pasteur taught (and this was VERY controversial at the time), there are bacteria and viruses smaller than you can see that can infect you and kill you. Handwashing was found to be extremely effective at getting rid of them. That is why it is taught today as part of the pandemic response.

(a) Wash your hands frequently

(b) Don't touch your face

Have you seen any of these instructions posted anywhere lately, say in the last year? I have, probably thousands of times. It works.

The reason they don't push the use of gloves is that most people don't know sterile technique to put them on and take them off. They'd screw it up and break sterility, rendering their efforts useless and wasting more gloves which were already in short supply. And for the general public, gloves (probably) are not any better of a barrier than their skin is. It's easier to sterilize skin with 30 seconds and hand sanitizer for an untrained person. Having 300 million people change their gloves 5 times a day is definitely going to run us out of gloves in like 10 seconds. (Unprepared FEMA all over again.) So they are shooting for risk reduction, not 100% perfection.

Like I said several times, no methods are going to be 100% effective for disease prevention, especially methods you give to untrained masses of people. This is just intended to be "good enough". Epidemiology just says that, in general, you have to get R0<1.0. If one single person doesn't wash their hands, then they touch their face and get sick, that doesn't take out an entire continent worth of people. But if 10,000,000 people refuse to wear masks or do any kind of social distancing or anything at all, it does.

Medicine and epidemiology are kinda messy, like chemistry. You never get all your reactants to react in an experiment. You never get 100%. But with this type of pandemic, you try for "as good as we can get it" in order to mitigate total disaster. And they have completely failed at most of that.

Edit: My own take is that we should have had a very brief shutdown in heavily infected areas of the country, and taught everyone the basics while we were at it. Been honest about the shortfall of emergency supplies. Geared up and had grandmas all over the country make masks while we were in lockdown. Then put up those plastic barriers and everything and practiced social distancing and worn masks. Contact tracing for infected persons. Encouraging people to quarantine if they felt sick. Those are reasonable responses. You don't have to shut down the country forever. BUT Trump weaponized anti-science deniers and refused to endorse masks early on. That was the exact wrong thing to do and it got out of control, fast. All he had to do was say "Here are some experts, listen to them. And buy my MAGA masks on my website for $20." He could have turned into a wartime president by saying "It is your patriotic duty to protect your fellow Americans by wearing a mask and social distancing." He would have easily won the election and he would have saved sooooo many lives.