I'm by no means a distance caster but from my person experience, unless you're already able to maximize your casting distance with mono, there's no need to use braid on a conventional for purely distance (if it's sensitivity of braid or capacity, that's a different subject). Practice makes makes distance. On the other hand, if you've reached your peak in terms of distance, switching to a braid with a lesser diameter might improve your distance. The problem then becomes convenience over the marginal distance you gain. Say you're able to gain 20 yard but sometimes have blow ups using braid. Is it worth the inconvenience when the fishing is heating up?
On a spinning setup, using limp braid allows the line to collect and get under control through the guides much faster. In addition, you can use a smaller diameter line thus improving overall distance. On a conventional, the line comes off in a straight line. Using a stiffer mono makes sense. You want the line to spring off the spool as it's rotating. Less resistance of the weight having to pull line off the spool. Even if you have mags, if it's setup to fast, you'll have a blow up. Also less packing of the line since braid can dig into itself. If you're using a conventional with braid and your cast isn't smooth, your potential for a blow greatly increases if your line comes off "bumpy" and goes through a series of small running guides. I've used a conventional with levelwind and have used 15# mono and 40# braid which is equivalent to 12# diameter mono.. At times I swear the braid cast a good 20+ yards further but blow ups do occur. Some were minor and I was able to untangle but after a while, I decided to switch back to mono for the convenience. Another option for using mono is using a smaller diameter line. If you change your line each season and are fishing a beach without a lot of structure, 15/17# mono can still land big fish if your drag is setup correctly. It will also give you a slight advantage distance wise compared to 20#.