Melting rocks into glass takes a lot more energy than melting scrap glass into glass. The ratio is not as good as for aluminium or other metals, but it's still worthwhile afaik.
As evidence: In general no one actually remelts recycled glass. Recycled glass is crushed and spread on top of landfills each night to prevent rodents from being active, and to reduce dust and pollution.
That's still considered "recycled". And this is after transporting and sorting! And yet they still don't bother remelting it.
"Seal holes in foundations of buildings or entrances to rat burrows with a minimum of 2 in. (5 cm) of reinforced mortar mixed with iron filings (from machine shops) or broken glass pieces 1/8 in. to 1/2 in. (0.3 cm to 1.3 cm) long. (You can put some glass in a tough paper bag and smash it with a hammer. Shake out the broken glass pieces into the mortar as you are mixingi t.) The glass or the filings deters rats from digging the filled holes out again before the mortar hardens."
"Common Sense Pest Control" by Olkowski pg. 633
Clear glass has value, while green and brown tinted glass has much less value.
“Glass recycling” takes all forms though, so now you have to sort optically, which has mixed results, or settle for “all recycled glass is now going to be brown glass”
That doesn’t even get into the part of how dangerous broken glass can be for workers along the recycling supply chain.
I don’t know if it’s worthwhile to recycle glass or not, but I do know it should be questioned rather than assumed to be an absolute benefit.