I totally understand the issue. Most people won’t notice the problem if all they do is hotspot their iPhone to say their computer and remain stationary/within wifi range the entire time. The problem with the iOS hotspot implementation is two fold:
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Aggressive battery saving. The hotspot turns itself off/becomes undiscoverable very quickly if no devices are connected. There’s no option to just keep it on all the time.
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The UI doesn’t make it clear that for the hotspot to be discoverable you need to keep the hotspot screen open until your desired devices have connected.
Behaviour 1 becomes an issue when you want to hotspot your iPhone to friends/family while you’re out and about. The other devices come in and out of wifi range and your iPhones hotspot will turn itself off when there’s no connected devices, forcing you to continually turn it back on over and over.
Behaviour 2 is confusing and a bit unintuitive. You open the hotspot setting, enable ‘allow others to join’ option, then close the settings app/lock the phone and expect the hotspot to just be on. Only after experimenting with this multiple times did I realise that you have to keep the phone unlocked and on the hotspot settings while the devices are stilling connecting. An alternative is to long press the wifi/data tile in the control center and enable ‘personal hotspot’ but it’s unclear how long it remains ‘on/discoverable’ for.
Are you using both Apple products? If you’re signed into the same iCloud then it will show up and tapping on the phone will enable the hotspot. Apple does their own special thing to make your other device discoverable to your other Apple devices.