I think this a good moment to 'gentlemen, a short view back to the past', and I promise that all that I say is relevant. Ladies, gentlemen and everyone else on the gender spectrum:
Back then (aka First GDPA Era, yes, we are currently on the Second iteration of the organisation), you had drivers actually come together and take the GDPA seriously. The GDPA was founded after drivers agreed that the FIA was not ensuring their safety in 1961, the midpoint of F1's most lethal Era (by sheer number of fatal accidents), the 1950s and 1960s. The drivers back then were united by the fear for their own safety and integrity, organising a successful boycott of the '69 Belgian Grand Prix and '70 (+ post '76) Nürburgring due to safety concerns.
The most remarkable event the GDPA ever performed was a successful strike of the 1982 South African Grand Prix. Picture this: you are a respected double F1 Champion, and after a two-year hiatus, you come back to F1. In the mail, you receive a form requiring you to fill it out, to receive your FIA Superlicense, allowing you to race.
On closer look, you realise that some clauses are concern-worthy. You'd be bound to a team for three seasons, you'd be required to declare your financial status, you wouldn't be allowed to criticise the FISA (another governing body similar to today's FIA), so consequently, there would be more reasons to strip you of your license.
You bring your concerns about the new regulations to the current GDPA President, and you, along with a few other drivers, don't sign. Even the drivers who have signed join your cause. The GDPA President announces that no driver will participate in any sessions at the track until the situation is handled.
Of course, you aren't taken seriously, so you hire a bus, everyone gets in, and you drive away from the track to a hotel. 29 mattresses are brought to a room, where the drivers essentially have a bunker. What follows is chaos. You (along with the GDPA President), attempt to negotiate with the FISA and FOCA Presidents; drivers are fired on the spot; some drivers' girlfriends are brought in an attempt to get them to get out of the hotel room; rookies are fearful about their careers and monetary fines; but you all (with two exceptions, one being a late arrival to the party) persist.
You get what you want, getting back on track in time for Friday's afternoon practice. Some monetary fines are handed out, and you are sanctioned for your behaviour.
You are Niki Lauda. With the GDPA President, Didier Pironi, you've just successfully rebelled against the regulations.
(from left to right; Didier Pironi, Gilles Villeneuve, Niki Lauda)
Following the strike, the GDPA is disbanded and replaced by an organization that falls out of relevance quickly. (very anticlimactic, but this is history)
Now, I could go into detail about how the Second GDPA formed (Summary, Ayrton Senna proposed it at the beginning of the 1994 season, only to suffer a lethal accident, and the GDPA was reformed after) and the details of its operations, but I'd rather engage the question:
"Why can't the drivers do something like that today?"
Simple answer? It just doesn't work like this anymore. Longer answer? As prev explained, drivers today can't unite even with a problem that affects all of them, and they're fine with the status quo as long as they can complain. Today's drivers are simply much more privileged.
Major difference between the past and today: F1 was a lethal sport, where the governing bodies cared even less about driver safety than today; It didn't matter if you had a grudge against one of the GDPA Directors; this was a matter of life and death, so you all got together.
In a hypothetical scenario, if you decided to strike today, then the team could fire you on the spot with no consequences; in comparison to the past, today most teams have more than enough reserve drivers to replace you, which wasn't the case during the '82 South African GP.
(one of the team garages during the '82 strike)
