Our Chefs encourage us to get our breaks taken care of. Even if only because they don't want to get fired for getting the property sued. Bad for business and a bit of a hit to money already made.
Most do want you on your breaks, it's more that at times it's simply not possible with out screwing over all your co workers. If you work in a bigger place it's generally not a problem but anywhere that is not a big name restaurant is generally luck if they are slightly over breaking even money wise so they can't afford more staff then necessary. It's just a part of the business honestly.
You can push for the break if you want and your chefs/managers will give it to you, but your relationship with your co workers will suffer when you ditch them for half an hour and it results in stations not being stocked or ready for the next rush. I've worked with a few people who thought those relationships didn't matter, they didn't last long.
It's a terrible part of the business when it can eventually lead to permanent problems for your employee's down the line. Most aches and pains that "disappear" are just you getting used to them, not recovering. And that'll cause problems for you further down the line.
If your business can't afford to hire a breaker, I doubt they can avoid to lose an employee for a long stretch because they're out due to and back or leg injury (likely given how long kitchen workers are on their feet and even non slip shows can slip) that requires surgery to "fix".
And that's not even including being tired causes people to make mistakes and mistakes in kitchens can be nasty as ***.
And being tired because of a break just means you should probably bring something to snack on during your break. Or even a small meal if your breaks are short.