Franklin Half Set Vs. Stacking

I like the idea of sets instead of random stacking because it would be a much more enjoyable journey.

Stack anyway.
Just take the best available pieces from your stack to build a date/mm set.

Do junk silver bins still exist? Never seen any at the LCS in my neighborhood.

I would much rather do the Franklin set. As far as junk bins go, if they aren't visible you should ask. I recently visited a new Coin Store and I didn't see anything. So I asked and then was given a huge bin that was behind the counter hidden underneath some random inventory that wasn't accessible by customers.

I agree.

Dealers cannot always display everything. For what it is worth, the last Ikes I bought at a coin show were not on the table. I would have missed out had I not asked.

A sale is a sale.

Why even have a junk bin if you are not expecting to profit from it?

I was looking through a junk silver bin at a local "Gold for Cash" shops as a repeat customer. After about two minutes, the owner that was working there said "I don't have time for this" and gave me a lecture for five minutes about his problems (note there was nobody else in the store). I had many bad experiences at this one shop, and this was the last straw. There are too many nice people out there to get entangled with the salty ones.

NumisEd, do not be dissuaded by the term "junk" silver. Also referred to as constitutional silver. The term refers to pre 1965 dimes, quarters, and half dollars containing 90% pure silver that have lost any numismatic value due to wear from circulation or desirability. Silver dollars are not normally sold as junk, referring to Morgan's & Peace dollars. That is because the silver content is higher and most retain some numismatic value regardless of condition.
Any LCS that I have visited in the last 40yrs has had a junk silver bin. Such as a bin of dimes, a bin of quarters, and a bin of halves. Simply ask the dealer if he has any "junk" on hand and is so, the denomination you desire. The common practice, in my experience is that the dealer brings you the bin or tray, and you select the coins within that you want to purchase. I avoid shops that do not let you browse the bin. Some ask what you want, like $10FV quarters, and they will go in the back and bring you out 40 quarters. The shops that give you the bin and let you browse are the best bet.
You would be surprised at what you may find on any given day. There are shops that purchase from wholesalers exclusively as well as others that purchase collections from estate's as well. Or perhaps melt price exceeds numismatic value, so people Crack open sets to sell the silver because it is worth more than the intact set.
Then you come in a few days after the dealers purchase, and those coins are in the junk bin. I have many proofs acquired right after liberation. Many, many nice hole fillers for many type sets. Very nice winged liberties, nice Walkers. And on and on.
Sometimes, I do not know how I came across this. Most dealers will examine collections for key date but not for varieties and errors. They don't have time for that.
In the end, when you use your silver for barter, no one will care if it is VG-20 or MS-65.
Go find a LCS that let's you leisurely browse the bins and makes you feel happy when you get home. If you stack silver it is for barter. If you plan to sell for fiat money when the price rises, you are an investor. I am not an investor.
I hope this helps.