I have the exact same problem. In fact it occurred with both sprint and AT&T iPhone 4s's, so it is definitely a hardware issue and not the network. My old android evo would always be recognized instantly without fail. The delay occurs with the phone locked or unlocked. I haven't noticed any difference. I thought it might be due to a weak 3 or 4g signal but can't confirm that yet. and yes, the HSPA+ is considered to be 4g... Data speed is really nice when it finally works. I wish it was consistent.
I've since resolved this problem - at least so I can cope with it without too much hassle.
You said your phone is unlocked. Do you have a passcode enabled?
In my experience and testing (Apple support has been useless on this problem), I've narrowed it down to making sure the phone is unlocked and passcode disabled. Either feature alone will block the WiFi hotspot. [By the way, I've also learned that Siri is blocked from reading text messages, etc. when the passcode is in effect - even if you are using a Bluetooth device that is already paired with the phone. Obviously, you must be the owner of the phone if you've pair your device to it.]
I went to my local Apple store on a Genius support visit. I demonstrated how enabling either feature blocks my iPad's ability to detect the hotspot, and disabling both allows my iPad to see the hotspot. The guy just said he had never seen that before, and that they are always learning new things. He didn't do anything to elevate the case to higher level support, like Apple engineering. I just left the store and that was it.
I've explained this to Apple support more than once and they never seem to be aware of it. I'm supposed to call to speak with a management level guy, but I haven't remembered to make the call.
So, I walk around with an unsecured phone all the time so I can conveniently access my WiFi hotspot. And I have to make sure the phone it unlocked until the connection is established so my computer or iPad will find it. Otherwise, all I can see is everyone else's equipment.
Maybe people don't use the hotspot much. Apple doesn't seem to care.
You are right, it doesn't seem like too many people use the hotspot otherwise we would see a lot more posts. I also haven't been impressed with the so called Genius's at apple store. I heard from employees there that apple gives the stores very little support and they are practically on their own to figure things out. Not a very good support system if you ask me. Back to the hotspot issue. Today it took me about ten minutes before my iPad would pick up the iPhone hotspot. I had the phone open at the settings page and hotspot showing that it was on. It was very frustrating because I never knew when it would kick in. It's very random because other times it instantly finds it. Also I don't use a pass code so I'm not sure how it affects mine. As for Siri, I still haven't used it that much, so I can't share any issues on that. If you find out anything more from the expert I will be interested to here what you find out. This is definitely a problem the iPhone is having with hotspot.
Wow, so you're struggling even with it unlocked AND no passcode? I thought I had it completely figured-out. Have you tried resetting your iPhone to factory - just for good measure? I can't imagine what would be different between our two phones - why what works with mine doesn't work with yours.
Weird stuff happens for sure. Two days ago, I realized that only one sound was working on my phone - the Ring Tone. All the other sounds were silent when I tried them. Phone support told me to reset to factory and, sure enough, the sounds came back. How one sound keeps working while the others stop is beyond me.
So, maybe a factory reset would be helpful in your case with the hotspot problem.
I also have this problem but don't use a passcode and the problem is not resolved even when the phone is unlocked. I've confirmed the problem is not with the MacBook (the network also isn't visible to my wife's Dell laptop.)
I often spend 10 minutes power cycling the phone, toggling airport mode and personal hotspot, changing the Wi-Fi password, and other settings until eventually the network appears on my MacBook's list of available networks. I am successful 80% of the time but have yet to determine any pattern.
Perhaps I should try a factory reset of the phone.
I'd definitely back up to iCloud and do a factory reset. It works well (just did it last night for another recurring problem). If that doesn't work, I'd take it up with Apple tech support.
Seems to me, there's something fundamentally wrong with the "S" phone. I tested the prior phone, the 4, and didn't have any trouble like this.