I agree that it's a software problem, but most vendors aren't in apple's position of controlling every single link of the chain.
I do think it'll get better over time. NFC/tap pairing will eventually replace Menu + Manual Madness, show-stopping bugs will get fixed, capability sets will stabilize, conventions will develop to smooth over variation in UI choices, "worse is better" decisions will be unwound, and eventually it'll be a smooth experience and people will wonder how they ever lived with wires. If my own experiences are typical of even a tiny minority of users, however, that day is still disappointingly far off.
Apple will probably do the Bluetooth equivalent to what they did with earphones: they switched the mic and ground wire, forcing earphone manufacturers to either support iOS or TRRS on the built-in remotes. I love my Macbook Pro and iPhone, but Apple can be a truly infuriating company.
You must definitely add investor pressure in all of this, and if history is of any indication, that pressure can and will kill any creative efforts. It's all about being first to market, making a big buck and having a lucrative exit nowadays.
Nobody is interested in the tech becoming more comfortable.
I think the problem is that in this case Bluetooth is just not fast enough to transfer large amounts of video data. What they should do is use BT to negotiate details of an ad-hoc Wi-Fi network and use that larger pipe to send the actual data.
You basically just described Bluetooth 3.0 + HS[1]. The Bluetooth connection is used to establish an 802.11 link, over which data is transferred. It's only (up to) 24 Mbit/s, so it's still slower than some (direct) Wi-Fi alternatives, but it's much faster than normal Bluetooth connections.
I just bought $40 bluetooth earbuds that required RTFMing to pair, don't hold the pair between workouts, take a minute to perform the ritual, and use friction to anchor themselves to my ear so thy fall off the moment I start sweating. Oh, and they need to be recharged.
I have similar stories for every single bluetooth device that I have ever tried, which amounts to probably a dozen peripherals and half that many hosts. I've had fleeting moments of "it's magic" to punctuate the sea of crap so I'm fully on board with the potential of the technology, but it has continued to mature at an obnoxiously slow rate.
Your bluetooth speaker setup works great for precisely your scenario - the speaker is paired with one only device.
It gets wonky if that single speaker has paired with multiple devices before. For example in a home, where you've paired it with your laptop, phone, iPad, etc. Try it out. Audio will cut off sometimes suddenly when it decides to switch pairing partners as another paired device appears in range.
I have a Sony bluetooth headset and it's amazing. It was around €65, lasts 40 hours of use (so charge once a week- every 2-3 weeks depending on usage), pairs with 3 devices and does it very well. I often move to another floor while having them on (construction work) or go out to the shed while the iPhone is in the bedroom on a charger, and it still works 10 meters in the yard. Best thing I've ever purchased, so there are good Bluetooth solutions.
I do think it'll get better over time. NFC/tap pairing will eventually replace Menu + Manual Madness, show-stopping bugs will get fixed, capability sets will stabilize, conventions will develop to smooth over variation in UI choices, "worse is better" decisions will be unwound, and eventually it'll be a smooth experience and people will wonder how they ever lived with wires. If my own experiences are typical of even a tiny minority of users, however, that day is still disappointingly far off.