Sure, co-working places can achieve that too. But if you're living in the same city as a company office, then might as well use that. :)

I've found that co-working even then is beneficial. There's usually a co-working closer to me than the office, so less commute, not to mention I don't like working in a place where a manager oversees everything I do, every break I take, etc. What if I get my required work done in half the time of my peers and then just chill around the office? That might be a problem in the office, not a problem in a co-working. I like some autonomy.

a co-working is simply an office paid by you instead of the one the company paid for you.

Actually in most cases the company pays for your co-working. At least that's my experience working for fully-remote or mostly-fully-remote companies.

Sorry for being so late to answer.

That's still an office paid by your company, with all the benefits that go to the company.

The company I work for before opening a new office for their employer has to provide:

- security

- daily cleanings

- insurances for all the people working there

- reception

- authentication and authorization (badge readers etc.)

- secure connectivity and storage

- water, beverages, sometimes a cantine if the office is big enough.

That's by contract (at least my contract).

If they are really going through the route of paying for your coworking they should sign a contract, which means a lot of bureaucracy and most of all it would force the employer to always use the same space for at least a few years.

So the better way is to ask for a pay rise to pay it by yourself.

If you can pull it out.