I didn't read all of the replies, so maybe somebody beat me to this idea, but:
I feel like most of the AVRs on the market today from the respectable brands are all at parity with each other in terms of features. I'd love more features, lower prices, stronger amps, more inputs/outputs/zones/etc, but I like to think about revolution, not evolution.
That said, I'd like to see a modular AVR platform. Build a system that is basically a chassis containing a "motherboard" with "slots", whose only jobs are to provide power, cooling, an incredibly high-bandwidth/low-latency/low-interference interconnect, a dot-matrix front display, and an interface designed with A/V in mind. The end user can install whatever modules they please. Modules connect into the slots on the motherboard and can optionally provide ports on the back panel. In concept, this is very similar to a PC with PCI-X slots. A module might be an amplifier; perhaps two channels, with speaker connections on it. Or it might be an HDMI input board, with perhaps four HDMI inputs on it. Or it might be a legacy input board, with component video and coax+optical audio, or an even older legacy input board with composite or S-video or plain old RCA stereo audio, or a 7.1 preout board. A Wi-fi board, an Airplay/DLNA board. An Audyssey board, a DSP board, a DTS Neo:X board. An onscreen GUI board. An output board with an HDMI out, or a legacy output board with component. Two output boards? Two zones. Add a third for a third zone. If you have enough slots and bandwidth, add as many zones as you want. Want analog audio to zone 2? Get a second DSP board (or an output board with one built in) and you've got it.
Manufacturers would sell chassis varieties empty as well as preloaded with popular configurations (at a slight discount compared to piecing the same setup together yourself). More expensive versions would include capacity for more modules and/or higher maximum bandwidth. There might be internal-only slots for processing-only boards, or front slots (with prettier cover plates) for those who care about front inputs. High end chassis might have an external super-high-bandwidth interconnect to hook up to another chassis, giving basically unlimited maximum expansion capacity.
Benefit to the manufacturer: vendor lock-in. Once a customer has outfitted a Denon chassis with a bunch of Denon modules, they're unlikely to switch to a Pioneer chassis the next time they're interested in upgrading. It's like how a professional photographer with a Nikon camera will basically never consider switching to Canon because he'd have to throw away his huge investment in Nikon lenses, flashes, and filters.
Benefit to the customer: no more worries about whether a new, modern AVR that offers the high-tech features you want like Airplay or 4K will also offer the legacy inputs or outputs you want.
Third party manufacturers could make modules compatible with the most popular chassis brands; you could have a Sony Playstation 5 on a module someday (probably only available on Sony AVRs), and your Dish Network DVR on another. The possibilities are enormous.
It'll probably never happen.