Why has indexed shifting displaced traditional friction shifting? I really don't like indexed shifters, at least on the front. They're harder to adjust, more sensitive to cable stretching, and limit the number of gear combinations you can use (because you can't adjust the front derailleur cage manually to not rub on the chain).

So.. why are they impossible to find these days?
There is no 'conspiracy' to keep friction shifters off the market just so that you have to buy the index shifters. It is simply a matter of supply and demand. Nobody in the OEM market wants friction shift gears because bikes with friction-shift simply do not sell. That leaves the after-market and you have a similar position there - the demand does not exist amongst people building up bikes/repair old bikes.

One reason why the replacement part market does not exist is that friction shifters rarely break, even 'back in the day' they were not a common spare for shops to stock in depth.

As for your front-shifting problem, you do have the outer cage 'flat-bit' parallel with the chainset and clearing the outer ring by all of 1-3mm? Without that accurate positioning it is unlikely you will get your front mechanism to work. New cables help, and if you follow the Shimano/SRAM/Campagnolo manual to the letter, making sure no dropouts or derailleurs are bent, you will have a chance of getting optimal shifting.

I know that a simple shift-lever adjustment would be easier, but that is progress for you.