The reason it works is because the brushes wear out, and when they get to the end of their wear life, the spring that pushes them against the armature inside the starter is about at the end of it's tension, so banging the starter gets the brushes to contact the armature just a tiny bit more, the springs to push just a tiny bit more, and you'll get another start out of it. This can work for quite awhile, but you really need to be careful with the banging, otherwise you can crack one of the magnets inside the starter and then it won't work so well anymore.
You can replace the starter (although it's a shame to trade in the OE Motorcraft starter as a core because they are so well built compared to the Made-in-China junk you get back), or if you're mechanically inclined or know someone who is, you can buy the starter brush assembly (pictured above) for $20-30 and have it installed. Note the brush assembly isn't known to the guys at the parts store counters as being for Explorers, it's for a lot of Ford vehicles but they'd rather sell big-profit starters.
It'd probably a little easier to use sockets and extensions with a breaker bar/flex hander to remove the starter nuts, it's possible to do with regular wrenches (not an adjustable or crescent wrench though) but it might be pretty tough to bust the nuts loose with a regular wrench due to how short they are. You could always just buy one "long" pro-quality professional wrench to use for the job, they are longer than most regular wrenches and so give more leverage.
If you want to DIY it might be worth your while to get a ratchet and socket set for this job and future work, otherwise if you want to pay someone to do the work, it should take all of a few minutes to pop the starter off, remove the old brush assembly and install the new one, re-install the starter and done. Even less time to just put in a new starter, although the $100-150 price of the starter makes the $20-30 for a brush assembly (and keeping the Motorcraft starter) the better deal. If you buy the ~$60 starter from DB Electrical (which IS a cheap made-in-China one), it should make it a fairly easy DIY affair, just taking the old one out and putting the new one in.