Oh dear. I love that this is now a thing!
Back in the days when remote controls worked through long wires, you could pretty much guarantee that when you pressed a button on the remote, whatever was supposed to happen would happen immediately. Sometimes there was an electromechanical switch in the way which could take a while to operate. Over the years the remotes became "wireless". The earlier ones with Infra-red connection were still quick, depending on complexity and implementation. Dedicated control hardware could help.
Now we have digital media devices, which are just computers of various types, with Bluetooth connectivity. Low and behold the whole thing has become slower, flaky and very clunky!
So what is happening in the car? You press a physical button on the steering wheel. The car's distributed computer system detects somehow, and sends it to the required device over a data bus of some kind. This at the very least, means detecting a physical switch, turning this into a code, putting the code on a data bus (I believe the CAN-BUS system is asynchronous? I don't know.) The control system decodes this off the bus, looks up where it has to send the command, finds that it is a paired Bluetooth device, re-encodes it and send it to the Bluetooth transmitter. The Bluetooth system has to connect, exchange handshakes, send the command. The device decodes the command and executes it. Many stages to go through. They may each be fast, but there will be some latency.
So you press the button, and it takes a second or two for a response. this is called control lag. Many years ago (I think over 20) I was at a demo for some remote control gear for professional film cameras. The device was a wireless remote to allow the camera assistant to operate the iris, focus and zoom on the lens without being tied to the camera by a cable. The operators hated it because of the delay. This was a direct, dedicated, radio link over at most about 5 metres (15 feet for those on the wrong side of the water!). I am not a camera operator and I hated it. Recently I tried out some Bluetooth headphones with remote for my music player and gave up after 20 minutes for the same reason. Slow and clunky. Quite frankly I can't see how you could make this any faster without designing dedicated hardware so the whole system was integrated. As far as I have been able to find out, these car entertainment systems us off-the-shelf hardware, and in some cases the processing is being done in more than one device. You could integrate the hardware and have only on software package, but it would still be slower that doing it with a wired control. I can't see a solution that the manufacturers would go for. Cost alone has driven the way things are now.
Very sad. Always two steps forward, and one step back.