I look at it like this,
a compound will outshoot any traditional bow. It is a designed machine that is made to make shooting an arrow very easy compared to shooting a trad bow. A lot of people who shoot compounds do exactly as you said. Why would they shoot a longbow when a compound will flat out blow it away?
A high end traditional style ILF engineered riser with complex limb designs will blow away any self bow out there in pure performance.
So it is very relative.
I have shot Olympic style ILF target bows for more years than I can count. I love the ease of accuracy. They are fun. I have camoed them and hunted all over NA with them. Enjoyed every second.
Now, I have some VERY beautiful custom built traditional bows. More than I should. If I feel one doesnt perform well enough to hunt an animal and be ethical, it is out the door. This has rarely been the case. They all perform very well. I may have to adjust my own form to make them work for me, but I love that.
I have hunted with them all and have been successful with every one.
. Whether the bow is considered ugly, not too concerned. I have a well known custom wood recurve by a VERY well known bowyer and its hideous. Someone ordered it that way. I shot it once and said, gotta have it. I hunt with it a few times every year.
So, my answer is not necessarily. If I had to keep only one,in my life right now, I'd pick my favorite custom exotic wood recurve. Its plenty accurate to take game and win a few 3D shoots. I LIKE it. I appreciate what bowyers can do today with mother natures wood. I like the artistic talent it took to create THIS bow. When I pick it up I smile, whether anyone else is around or not. Is it as accurate as my scoped 30.06 or my best ILF tournament rig in my hands? No.
But since this is hypothetical, i will gladly keep and hunt with all my bows...ILF,longbows, recurves, takedowns, one piece, snakey,knotty selfbows....love 'em all.