I see so many comments here about how people do not have time to shoot a recurve/longbow and I just want to make a comment which is not ill intended at all. First, think about it, you will take away pretty much all of the time that is spent "tinkering" with your setup if you move to traditional, this time could be spent practicing. Second, you will find that practice sessions are not quite as long with traditional mainly because you do not aim as long. Third, I would go out on a limb and say that a person with consistant practice session of every other day shooting maybe 3 dozen arrows a session, could be pretty accurate to about 20 yards in maybe 4 months or so as long a consistant quality practice sessions are followed. In other words, I don't think it is as bad as it seems.
I also noticed a comment about the price of traditional bows. And yes they can cost as much as a compound, even more. I know I paid over $500 for my last longbow and the same bow is going for 700 now. I could have sold my bow for a few hundred more then I paid for it the day after I received it and still can. But, the bow is made directly for me with the wood that I picked out, my specific draw length of 31" ,the poundage, and the length. The boyer that I bought it from is in high demand right now and isn't even taking orders at this time. He makes everything from start to finish on the bow. But these are the top of the line bows. For someone starting out, I would suggest something used. Usually about $100-150 could get you started until you know for sure if you like it or not.
Here is a picture of my OL Adcock longbow.