The green jersey I've never really attached that much value to, especially since the move to even further sprint-weight it; we can always know who the best sprinter is at the Tour, they're the one winning the most stages. The other thing was that for several years it was so comfortable for Sagan because he could get to intermediate sprints no other sprinter could that for several years he'd take the jersey on stage 2 or 3 and nobody would even really bother trying to take it off him, so for years there's been very little competition for it, and the one year that there was, Sagan fell foul of the only time the commissaires policed the offence and not the outcome and got relegated for an irregular sprint when there wasn't a crash, causing a lot of complaints from fans because the competition for the jersey had been ruined. The GPM was massively devalued thanks to the success of the Virenque method and some godawful course designs in the late 2000s that meant that the rules at the time skewed the competition. Back then points were doubled on an HC, cat.1 or cat.2 if it was the last climb of the day (regardless of where in the stage it was), and there were no bonus seconds at all. This was largely as it was the péloton à deux vitesses era and so allowing breaks to take most of the main stages kept the French riders involved, people like Casar, Fédrigo, Dessel, Riblon, Moncoutié and Moreau being key protagonists in these stages. But it also meant that if you threw out a stage like 2009's execrable Tarbes stage or 2010's Pau stage, with the final mountain over 60km from the line, no GC rider would ever take action in those stages, but the mountains gave out stupidly high numbers of points, meaning that the GC riders never really bothered considering the GPM and you ended up with riders in totally irrelevant GC spots winning the prize which was not how it was intended.
Since the reconstruction of the classification in 2011, this seemed to work OK for a while, but the heavy exaggeration of the points for the MTFs meant that on occasion a GC rider could win the GPM almost by accident, as Froome did on one occasion. Things like Majka's wins in the classification, and Quintana in 2013, seem to be what they were aiming for, but as time has gone on and the course has had fewer TT miles (meaning the specialist climbers have little reason not to think of themselves as GC men), stage designs have become more backloaded and we have fewer multi-col stages with true HC and cat.1 climbs mid-stage (plus the over-categorisation of a fair few last climb of the day ascents) has meant that it's far too easy for GC men to win the GPM without even trying to - in recent years we've had people like Wout Poels, Michael Woods and even Richard Carapaz - great climbers one and all, and people who would seem perfectly appropriate KOMs - working to collect points for a whole race, getting in breaks and sprinting out summits the way we expect to see GPMs fought out, only to see a couple of days of breakaway effort wiped out in an instant by Tadej Pogačar winning an MTF which is worth as much as every other climb in two days put together. This year they've attempted to rectify this, but the way they've chosen is to overcategorise summits the break will take, and undercategorise MTFs instead.
Maybe it's time to just get rid of the double points for the finish, since GC men are contesting each summit now? Or maybe it's time to reinstate double points for the last climb even on descent finishes. For the moment, it's too easy for the GC guys to win it without trying to, and nobody in the break thinks they can win the title so they don't really contest the points either, so you're left with somebody getting into the jersey early in the race in a random break and holding it almost uncontested like it's a metas volantes jersey in the Tour of Britain or something until the GC guys take it, like Cosnefroy in 2020 or Abrahamsen this year.
The other thing of course is that wildcard teams have been all but wiped out. It's massively hurt the spectacle of flat stages, because we're increasingly seeing no break at all, because with their invites at all the top races guaranteed, none of the sponsors even need the airtime. A few days in a classification lead was really important to teams like Agritubel, Saur and their likes and they would enliven those stages to battle for those points and that airtime in a way that really isn't possible when the "wildcards" are a team like Israel-PremierTech who know they're going to all 3 GTs and all 5 monuments if they want, because despite being a "wildcard" the organisers are forced to invite them.
So, to sum it up, the value of the 'king of the breakaways' has been ruined by Premier League Cycling meaning that there are no teams whose primary interest is breakaways anymore, the points system was a reaction to circumstances in cycling fifteen years ago that is probably due an overhaul due to the change in circumstances in cycling since, and the kind of people who ought to target the GPM simply don't because it's too hard to win without being a GC man - but as long as the GC mix is reduced to such a small number of competitors, without incentives and means by which to win the secondary classifications, it reduces a large percentage of the péloton to irrelevances. UCI, ASO and their like need to find a way to make the GPM relevant again, so that riders outside of the two or three over-powered super teams think it worthwhile to contest it. Maybe give some major UCI points for it and tilt the points balance away from the GC, so that the teams whose WT spot is in jeopardy want to slug it out, maybe get rid of bonus seconds at the line again so more breaks are allowed to settle stages, maybe more multi-col stages, maybe not such a stingy amount of points for cat 2/3/4 climbs to mean that they aren't rendered irrelevant by a single cat.1 or HC climb, maybe even just more TT mileage so one-dimensional climbers are forced to make more of a deal of the classification. But they do need to do something for the competition to regain some level of relevance.