I own a small business and have worked for small businesses, and it's my experience that checks make the world go around in the woodworking field.
All of the shops I've worked for have paid me by check - nobody wants to screw around setting up direct deposit for one or two employees.
Several of them pay suppliers by check; suppliers don't want to take the hit on credit card fees.
And all of them take checks for payment from customers regularly (and I do to), for the same reason, among others.
The only downsides I see to cheques is that they're insecure and that there might be insufficient funds. If you're dealing with a trusted party (or at least somebody you reasonably believe to be acting in good faith), those are basically non-issues.
The upsides are pretty extensive:
1) They don't require carrying around large amounts of cash
2) They don't require third party cooperation (at least to write)
3) They don't require internet access
4) They don't require any sort of set-up, which reduces the friction for one-time or infrequent transfers.
5) There's basically no fee for the volume we use them in [0] except for buying the cheques.
6) If a payer does bounce a check (unintentionally) the payee can insist on a more guaranteed form of payment in the future. The friction is added to the party that screwed up in the first place.
Edited for formatting and to add:
All of this requires an informal web of trust. I've definitely used cash for one-time large transactions with people I don't have in my network. I've sold a car for cash to a random private person and bought a bicycle with cash from a different random private person, for instance.
[0] My business checking allows enough free transactions a month that I should be covered for a while; if I start exceeding that, I probably won't be super-worried about the cost of the fees)
[1] A buddy worked at a cabinet shop whose plywood supplier wouldn't take their checks. They switched to counter checks or money orders, or something else that guaranteed sufficient funds at the time of issuance. Hypothetically they could have gone to another supplier. In practice, finding a good supplier is a lot of effort, there aren't many in the first place, and word gets around fast if you make a habit of burning people without making it right.