It was once a very common practice to turn cranks. Engines hold up better today so it is not as common.
In high school I worked for an auto parts store that included a machine shop and was involved with helping the machinist. He didn't have a crank grinder, but he delt with a shop that did when he needed that type of service. I've also been involved with hot rod stroker kits that were made from welded cranks.
Yes, it is practicle to build up a crank with welding and then grind it down to size. As with any welding, it must be done correctly, and when done correctly, it is just as good as a non welded crank. Also, there is plenty of strength in the crank to be taken down slightly to the first or even second undersize. You must use bearings that are made for the new diameter. If not ground correctly by leaving a radius at the edges, it can weaken the crank, but your crank grinder should know what is necessary.
Balancing is always nice. It is more critical on an engine that spends a lot of time in the upper rev range. It may not really be necessary if you stay with stock pistons and other recipricating parts. It is essential if you change piston weight and/or rod weight.
