I am creating a new Arduino based board, based on the Uno. It will be the same form factor as the Uno. It might become available to the public, so please don't submit an idea if you don't want it to be used in something that may be sold.
What would you do different if you were redesigning the Uno?
Why make it the same form factor as the Uno ?
For ease of using the many Uno shields on it.
There are so many Uno clones available that it would not be worth producing your own
You would be better off producing a board with much the same functionality as the Uno with a smaller, breadboard friendly form factor and a range of your own shields. They do not even have to be the full size of the board
Whilst the Uno has been a success it is clumsy to use, the pin layout is non standard, there are not enough 5V and GND pins available and why LED_BUILTIN was not put on a PWM pin has always intrigued me
For my own use I designed and built a PCB into which is plugged a Nano. The board contains 4 permanently connected buttons, 4 permanently connected LEDs on PWM pins and a permanently connected pot on A7
There is a 4x4 keypad on the PCB connected to pins of the Nano but unless the Keypad library is used they are free for general use
All of the free Nano pins are brought out to pin headers and there is a 5V and GND pin for each of them
The board has served me well for my own experiments and for providing help in the forum
I also have a similar board for the ESP32 but without the keypad, but added a 4 way voltage level shifter and an I2C connector into which an OLED screen can be plugged. Because the power pins of such screens varies in layout, power to its socket is set by jumpers as is the presence/absence of pullup resistors
Were I designing either board again I would incorporate 8 WS2812 LEDs too
But would you bother with a Nano at this point, or move to a processor from this decade? The Nano is long in the tooth, though I would agree for 95% of the things I think up to use it for in my world, it is still adequate, and so convenient.
C
The advantage of the Uno/Nano family is the vast amount of material and expertise available online and the fact that they work immediately with the Arduino IDE. No need to install support for extra boards which complicates things for beginners
Power circuit like the Nano so it's safe to connect 5V and USB at the same time.
Multiple connections for I2C and SPI (not two for each as on the R3); for I2C add pullup resistors that can be disabled with jumpers.
Just some thoughts 
I would add WiFi and BLE functionality. I also would make the LED on pin 13 a neopixel type led to allow color changing. Maybe some built sensors that have switches so that they can be enabled and disabled according to pin needs too......
The main problem is surely that as soon as you redesign the Uno you no longer have a Uno
You might as well start from scratch
Shields are generally far larger than they need to be and constrain the design by forcing you into using the original Arduino form factor. They also have the same problem as the PC-104 mezzanine boards that came before them: they must be designed to stack and either not use the same I/O pins, or have a way to redirect I/O. You're far better off using something like the Sparkfun qwiic or Seeed Studio Grove systems. Those are far more flexible in terms of part placement and use fewer I/O pins.
In the end, you do you, but I'd at least want to put some thought into what the end goal is.
Maybe too far outside the box but perhaps a Raspberry Pi Zero format board that stacks onto the 40 pin Pi connector. The Arduino IDE runs on the Raspberry Pi so you could add I/O with realtime capability to the complete OS of the Pi. A Gertboard that wasn't huge.
My five bobs worth …
There is now a vast range of Arduino products , of different performance some with sensors , Wi-Fi , Bluetooth whatever, some close to bare bones - many have facilities and performance beyond what my brain can deal with .
The UNO is still a great product and what I used to get into this stuff , sometimes with shields - That really is it’s market
I can’t think of what extras you might need .
Once you get into this stuff , really the next step is making PCB’s to serve particular tasks that you want - users always want something extra or don’t need some features they get .
As an aside - it will be very difficult to make boards cheap enough to compete with what is out there unless you are into serious factory type large quantity production ( you won’t be able to get the parts either !!!!! - I’m on 18months for buying 328’s from Microchipdirect )
How many would you do then?
That would be nice... My only issue with that is how power hungry those are. 45 mA!! 
I'm trying to get a Kickstarter (once my ideas are complete) which will fund 500 of these. That will drop the price to about $12-15 (AUD) each. add a couple dollars for profit, and they are still less than $20 each. I know I should be getting more than a couple dollars of profit, but what I'm saying is that I can make them cheaper then the genuine Uno.
Have you looked at LCSC? They have 5356 in stock, ready to ship...
I don’t own one shield.
Bought 50 Arduino Pro Minis when they were selling for $1.75
Now concentrating on ESP32s.
The UNO is gone but not forgotten.
My beginner remark: Can't have enough PWM pins. Then again, not having enough forces you to think outside the box.
I'd assume that if a different board shares the same form factor, it probably couldn't be 100% compatible with Arduino pins, so the form factor point would be moot.
I have an earlier version of this Uno clone: Freaduino Uno Rev2.2 - Mikrokontroller Arduino Boards Arduino kompat. Boards - Boxtec Onlineshop
The text is in German but you'll see it has a number of useful features including multiple sets of parallel header pins, a buck converter instead of a linear regulator allowing use of power supplies up to 23 volts and it has a 3.3volt / 5 volt switch (note that 16MHz at 3.3volts is light "over clocking")
This is my idea:
Some recommendations:
In the box:
