Is there any reason not to keep the stock oil cooler and stock oil filter setup when running a full flow case to an external oil cooler?

The reason I'd give is when you tap and plug the pump you actually enlarge the outlet hole and that hole sits in a little deeper than the stock T4 pump. You are risking a leak directly into the case where you definitely don't want a leak.
It's likely is a low risk but why take it?

The other thing is the stock console has a bypass valve that is redundant, as most modern oil filters have a built in bypass valve.

Personally I prefer using the full flow cover method, but if you want to keep the stock console I'd recommend using a filter adapter.

You do realize to run a full flow cover on a 914 you have to modify the 3/4 side engine mount to clear the outlet.

Yes, I realize one of the engine bar mounts needs modification. I purchased a set of modified engine mount brackets from Mark Henry.

So, you're saying to eliminate the stock oil filter console with a block off plate and keep the stock oil cooler in place. Then add a remote oil filter mount inline with the oil line to external oil cooler plumbing?

The full flow setup with the modified pump would bypass the stock oil filter console. So it's one or the other on that. But you can modify the stock oil filter mount to plug/block/lock the ball valve bypass. That'll make your stock oil filter into a full flow setup.

You can keep the stock oil cooler with either setup, and I've never heard a reason in support of removing the stock cooler that makes sense to me.

Doh!
That's right you did! One to many chairs to the head in the ring....

Just use a remote filter mount , super easy and cheap.
Use type 4 filter WIX (NAPA gold) or mahle.

The best low cost hose is Parker pushloc with real pushloc fittings. No clamps!
I've used parker pushloc for years, no clamps, never a failure.

Note any hose can fail from improper installation, like not using grommets, sitting on an exhaust pipe, sharp edges, etc

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