Pairing is the Problem
There are two issues when "turning on" a Bluetooth device. One is the traditional power. The second is pairing. Pairing tells the device to look for other Bluetooth devices and connect to them. The first time with a particular device pair there is usually some sort of confirmation required. Without this step, multiple people with cellphones, wireless speakers, etc. would all get jumbled together - which would not be secure and also cause a lot of confusion.
Typically a device will remember the last device it paired with, so that when you turn it on it will automatically find & connect to the same device if it is in range. But to avoid the process happening unnecessarily, the device will typically require a long-press. That allows the same button to be used for other functions. For example, my Bluetooth headset requires a long-press for on (including pairing to an existing device) and uses a regular short-press for answering/disconnecting calls.
It is certainly possible to have a device which has a more traditional power switch with the pairing function handled differently. But you typically won't find that on a $6.99 receiver. The alternative, as suggested by another answer, is to build/program a device to simulate a 5-second long-press.