I have used level fly lines since I was a kid. I don't use them exclusively as I also use double tapered and weight forward lines. But, I have several vintage reels spooled with different weights of level line. I haven't looked for any in stores for a long time, but I would suppose they would be hard to find. I know level fly line is still made but I don't remember which companies still carry them. I'm sure there is not much of a demand for it. I find most of my level lines on the auction sites as slightly used or as NOS, and there are always dozens of them from which to choose and for very good prices. I have some by Scientific Anglers, Cortland, Gladding, and a few others. I have also obtained several that were on some of the vintage reels I have purchased. Many of those lines are worn out and useless, but some are very serviceable.
Now, about fishing and casting with them. If one is dry fly fishing on gin clear streams for spooky trout, then he/she should probably not use a level line. Lines with a front taper allows a gentler presentation of the fly and will provide more strikes and be less likely to spook a fish. But for just about every other fishing situation level lines work just fine. I have found them to be easy to cast and I can get all the distance I need, which for the small streams I fish is not much. When I lived in Florida and fished the flats around Sarasota Bay, I used a vintage Scientific Anglers System 8 fiberglass rod and a SA Wet Cell 9 weight level sinking line. That line with that rod would cast a mile and with little effort. Caught lots of sea trout, redfish, snook and ladyfish with that rig.
Why are level lines pretty much now out of fashion? I believe it is marketing. Several years ago, in the 1960's I believe, the Orvis Company convinced fly fishermen that they needed weight forward lines. I have nothing against Orvis as I believe they are a great company and they sell great products. I have several Orvis reels and bamboo rods. From then on, weight forward was the way to go and even double tapered lines took a back seat to the WF lines. Now there are new WF lines that are very "specialized" for special fishing situations. The advertising hype on them have caused them to sell and sell well at ridiculously high prices; not because we need them but because we think we need them.
Another reason I like level lines is cost. I can buy new or nearly new level lines from auction sites for a fraction of what the new WF lines cost. I mean like less than $10 (sometimes a little more) as opposed to $60 or more for WF lines. And I am talking good quality from known makers, not the cheap over seas stuff. The level lines work for me though YMMV. Remember it is your rod and your reel and your fishing situation so use the lines you like. There are many many lines from which to choose, but you might want to give level lines a try.