Indexed shifting keeps the rider's hands on the handlebars. Indexed shifting also correlates with a move to integrated shifters for road bikes, so the hand position doesn't move, at least on the hoods and drops.
I can imagine some sly race tactic in the 80s with a rider timing their breakaway to coincide with a gear change by other riders in the group. Having your hands on the brifters means your hands are not ~30 cm away from the bars, and you're faster to respond.
Modern bikes have 10+ gears across the back, that's a lot more positions and a friction lever would have narrower "good" spots for each gear making accurate changes slightly more difficult.
With that many gears, it is more common to change up/down to a slightly different gear for comfort or power. If the shifter is further away and needs a more coordinated movement, you're less likely to do it. An older 5/6/7 speed bike might have 3~4 tooth jumps between some gears, so the cadence can change a lot compared to a single tooth jump, which is more common when there are more gear cogs across the cassette.
In short - fewer gears meant fewer shifts, and riders might have been pedalling slightly outside their preferred cadence to maintain the bunch's pace.
In addition, keeping your hand position still would be more aero - leaning down to downtube shifters will move the whole upper body. Even stem shifters move the whole arm, changing airflow.
You can doubtless get friction-shifters still but they are definitely less common. Properly tuned indexed shifters work very well, and are a gateway to fully electronic shifting which is functionally identical for the rider.
Summary moving the shifting to the brake lever forced the use of indexed shifting.
this answer applies equally well to pod/thumb/trigger shifters on MTBs, but there's less "race craft" in MTB and more riding technique, so reacting quickly to changes in the peloton is less important.
Also, MTBs never really had downtube or stem shifters, their friction shifters were normally bar-mounted levers so were closer to the grips.