If I get a metal hose like this, can I leave the faucet on?

Yes, if it’s a quality nozzle. I leave my faucet on all summer. My nozzle is a fairly cheap one, and drips, so I also have something like this https://www.walmart.com/ip/iOPQO-Water-Sprinklers-3-4-Connector-Super-Hose-Off-Inch-Heavy-Brass-Garden-Duty-Shut-Patio-Lawn-faucet-hose-connector-beauty-teeth-Black/1275374517?wmlspartner=wlpa&selectedSellerId=101269178 that I attach the nozzle to.

Will it not burst the hose?

It never has. I turn off the water at the house before the first freeze.
I have had the same on-off thing for a few years now, and it’s fine.

Thanks. I’ll run it past my master plumber.

Yes. I do it.

I do also.

I leave mine on all summer.
I turn off the tap when there is a chance of freezing weather.

Yes, you can. I installed a ball valve inside the garage where it stays warm and just leave mine on all the time except for winter. I’ll shut it off if we are going to be gone for more than a day.

In the past we’ve only used rubber holes and if we leave them on they spring leak. Will the hose shown in the details do the trick?

The weak link in that chain is the nozzle. Most hose nozzles are not designed to hold the water pressure 24/7/365 without leaking. Also, depending on where you are (if it gets cold) it would freeze in the winter and probably rupture.

But honestly, I don’t think the hose matters that much unless you have a regular hose that is starting to dry-rot/embrittle. You could hook up a regular hose and do the same thing with it, IMHO.

They have hoses on Wash Machines made of metal or rubber. They are left on and pressurized for years without issues. The nozzle is the weak link on that product.