Most of this isn't correct.
Bird & wildlife photographers don't use Live View.
Of course they do. I've been doing it for 8 years and I use live view a ton. Live view doesn't mean single handed use and you can use one hand to support the lens and the other to control the camera. Again, many of my shots wouldn't have been possible without it. I sometimes take pics of squirrels while the camera is almost ground level and I don't wanna crawl on my belly to do it. I also lift it above my head for birds and I'm not 8 ft tall and don't think most photographers are.
The grip isn't big enough to accommodate your whole hand. That makes it more difficult to support the weight of the camera & long lens. (D500's grip is larger. Add the OEM battery grip for even more real estate.)
I have pretty big hands and never had an issue with the A6700. I actually like that it's compact and easy to travel with.
Not really a meaningful feature for me. I mean maybe for a wedding photographer that could make a difference but not in wildlife.
You can use the D-pad to move the focus point and you can tap to focus which d500 doesn't support.
No function buttons on the front
There are multiple custom buttons and a function button on A6700. Almost everything is customizable too.
Maximum 7 fps burst rate shooting lossless compressed raw.
11 fps, not 7.
1/4000-second maximum shutter speed with mechanical shutter
I've been a photographer for 8 years and never ever used 1/4000 let alone 1/8000. Even 1/2000 can freeze chopper blades in motion. I really don't view this as a meaningful advantage.
The batteries are cheap and last well over a thousand exposures on a charge. I've taken 2k on one charge.
Migrating from the D500 to an A6700 would be a lateral move from an image quality standpoint and a step backwards from a user interface perspective. While the D500 has a professional user interface, The A6700 is an enthusiast camera.
None of this is valid or correct. The A6700 has a slightly higher res and higher DR sensor. The D500 sensor is fine, even though it gives you less room to crop, but there's far more to a decent shot than the image sensor. Features like better AF, IBIS, the ability to select the exact kind of subject you want the camera to track, and things like focus stacking (for when you're photographing insects and small animals) can be the difference between a good and an unusable shot.
My first camera was D7200 which has a pretty close UI to D500. The A6700 menu and interface is not only more mature but also more customizable and way more feature rich. This might be the worst point you brought forward.
Bird & wildlife photographers don't use Live View. When you're holding 6+ lbs. of photographic equipment in your hands, the most effective and comfortable way of supporting that weight is with the left hand supporting the lens, the right hand holding the camera grip, and the viewfinder up to your face.
This makes me think you've never used a bird lens? You can easily use live view, and you have in many situations. Using one hand to support the lens at the tripod collar and the other to hold and control the camera.
A 26MP camera has a 14% resolution advantage over a 20MP camera. That's what the laws of physics and the math tell us
What math??
26.2-20.9 (exact mp numbers from Sony and Nikon) = 5.3
20.9 * 25% = 5.225
This is how you do the math. The A6700 sensor has slightly more than 25% greater res vs the D500's.
The laws of physics have nothing to do with this, it's the most basic of math calculations.
Rather than bury the OP under hyperbole, let's provide them with some factual analysis relevant to their inquiry.
No disrespect whatsoever, but so far there's been very little factual analysis.
For the sake of argument, let's say the A6700 has better autofocus.

For the sake of argument?
Have you ever used a modern Sony camera? A canon R7 or R6 II? Do you understand why AF is much faster and stickier with these mirrorless cameras?
Not only do they use far better AF algorithms, but they also have way better hardware, with Sonys having a dedicated npu chip for af and subject recognition.
Not even the biggest of Nikon fans would claimit holds a candle to A6700 when even the much newer Z50 doesn't.
Let's say its hit rate for birds in-flight is 90% while the D500's is 75%. At 7 fps and shooting lossless compressed raw, the A6700 buffer maxes out at 23 frames after about 3 seconds. 23 x 0.9 = 21 frames.
Considering that the A6700 does 11 fps and not 7 (I dunno where you got that number) this is another completely incorrect calculation.
You're joking, right? The D7200 is "pretty close to (a) D500 in...ergonomics." The D7200 has Nikon's enthusiast interface. The D500 has Nikon's professional interface and build quality, not to mention a superior autofocus system.

https://cameradecision.com/topviews...0-vs-Nikon-D7200-top-view-size-comparison.jpg
Have you held either of these yourself? They're literally almost identical in terms of grip and body size. No one's talking about interface or af when it comes to these 2.
You don't use your camera to photograph birds or wildlife, either. The OP does. The A6700 is a lateral move in image quality and a step backwards in ergonomics.





https://postimg.cc/gallery/v4wBKKk/a0e742a1
Here's a sample of the wildlife and bird pics that I've taken. I literally specialize in macro birds and wildlife/animals. That's like 90% of what I do with my camera. I've also used both Nikon and Sony (3 Nikon bodies 2 Sonys). Yet another thing you got wrong.
The A6700 may be better for some genres. It's not an upgrade for the OP's usage. At best, it's a $3,300 lateral system change.
It's better for everything. Whether the upgrade is worth the money for op it's highly subjective.
Your post got pretty much everything wrong from the math calculations to your assumption regarding my experience. Again, not an ounce of disrespect meant, but you seem to have done the comparison based on what you think you know rather than what these 2 cameras are capable of.
The D500 might very well be totally adequate for op, to the point that an upgrade is a waste of money. This much I'm fine with of course, but saying the D500 is remotely close to things like A6700 or R7 is completely incorrect.