I've relied on my iPhone 4 and now 5S for hotspot duty for years now. It's very reliable and yes, runs without the screen on, and even on my 4 it would work fine with other apps also using bandwidth. It's a lot faster on the 5S thanks to LTE, which of course the iPhone 4 didn't have.
I'm on AT&T, though. Verizon won't do data at the same time as voice, as far as i know.
Speaking of Verizon, I first went to the iPhone for tethering after too many frustrations with a company-provided MiFi on Verizon. The iPhone works way better and is one less thing to carry (plus a charger). It is also significantly cheaper to pay for data tethering than carry a separate device with a separate data contract. Now I routinely offer tethering via my iPhone to colleagues who can't get their MiFi to connect.
I'm on AT&T, though. Verizon won't do data at the same time as voice, as far as i know.
Speaking of Verizon, I first went to the iPhone for tethering after too many frustrations with a company-provided MiFi on Verizon. The iPhone works way better and is one less thing to carry (plus a charger). It is also significantly cheaper to pay for data tethering than carry a separate device with a separate data contract. Now I routinely offer tethering via my iPhone to colleagues who can't get their MiFi to connect.