Technically you could remove the front derailleur (“friction system”) but as has been pointed out, you will severely limit your gearing options. Personally, I have a 21-speed mountain bike, but never use six of them since that would make my chain flex sideways too far, and there are a few more that are iffy for that reason. In your case, you would be turning your 10-speed into a three-speed.
Given that I have lived most of my life in hilly places, I find it less of a hassle to fix an errant front derailleur or shifter than to find one chainring that will work on level pavement and killer hills. At least you don’t throw mud into the mix… or do you? I could never abide by only having one chainring, or even two; I need three rings and at least six cogs on the rear (18 speeds) since I hit a range of stuff.
But that is me. There are people who swear by “fixies” that have only one gear, no freewheel (the pedals are always moving as long as the wheels are turning) and many have no brakes, relying on the rider’s legs stopping the pedals and therefore the wheels and hopefully the bike. You don’t see them near the hilly parts of town very often and those fixie riders that do hit the hills are in great athletic condition.
So, to answer your question of whether that part is necessary, it depends. What shape are you in? What sort of riding do you do? Over what terrain? Is there a happy medium between your preference for simplicity and your riding needs?