No system is perfect at this. Life is full of compromises.
As stated already, much is how the soundtrack has been mastered, and you need to pay attention to this. If you're listening to a BBC transmission, it's likely in stereo. So the speech element is not separated so no amount ot tweaking, AVR or not, will resolve this successfully.
But often the biggest culprit for speech/sound effects disparity is in movies where the original master has been designed for full range in a cinema and if it's a 5.1 or 7.1 mix, this is easier to address. Although I would argue that speech is often too quiet and muffled in the cinema too, with effects gut-wrenchingly loud at times (like Interstellar, which I enjoyed listening to at home much more, it was sufficiently quiet to actually hear it).
My own AVR has a control app that can boost the speech element separately. You can download the app and view it in demo mode if you want to try it: "iControlAV5" on Apple's App Store. It also offers a mode called "Optimum Surround" that compresses the dynamic range and can minimise the scrambling-for-the-remote problem. But with the worst movies, you won't solve this completely so don't think an AV receiver is the panacea for everything. But you do have a great deal more control than a stereo amp. It was the main reason I got rid of my stereo set-up some years ago.
Some would argue that the best of both worlds would be to use the AV receiver for movies, then use the pre-outs (available on some, but not all AV receivers) into a stereo amp for front left & right channels. Then use all stereo only sources directly into your stereo amp. This is easier to implement if your stereo amp has either a "Home Theatre Bypass" input that turns one input on the stereo amp into a power amplifier for your AVR, or at least if you have a digital volume control where you can set your input volume to a specific and memorable volume each time you use the input from the AVR.