To each their own. I prefer having the ability to adjust things from 1 central source. I'm prone to losing remotes.

My preference is for devices to be as simple and reliable and end-user repairable as possible. I have an aversion to any kind of appliance that might be dependent on someone else to update software or maintain a network service to keep operational. No software dependence at all if possible, just a basic microcontroller and firmware. Again, there's nothing to this that needs to be any more advanced or complicated than the functions of a basic alarm clock like this:

Instead of setting off an alarm, we're activating the feeding mechanism. Dead simple. Hell, you could probably make this yourself by wiring the alarm from a clock like this to a motor that moves the feeding mechanism.

Also, how would you do such a remote. You would also need a screen for feedback etc, which puts you back at square 1.

Nah, there's no reason feeding times need to be any more granular than per-hour. You can show that with a 2x6 grid of 12 indicator LEDs, with a 13th AM/PM indicator. On lights indicate hours when feeding will activate. You could have that on both the remote and the feeder, cheap and easy. Maybe you have a 14th indicator that lights up if the food in the storage bin is low and needs refilling.

Also, a remote would be considerably more expensive than the extra cost of a ZigBee/Wifi enabled microcontroller.

Definitely not, because it's not fair to count the cost of only the link hardware on the feeder, you have to account for the cost of the rest of the smart home system to operate it. A remote like this is dirt cheap:

You're over thinking what this really needs to do. It's a timer that activates a switch, that's all.