Proof of work allows the history of transactions on the network to be considered secure (ie, immutable).
When measuring the security of any thing, what we are ultimately asking is how much energy will it take to defeat the security system? The more value being stored, the more security we will desire.
The bitcoin network consumes energy in a very quantifiable way, at least compared to the traditional financial networks. As a miner, a large portion of your overall costs would be electricity, and this electricity is converted into security with increasing efficiency (each generation of ASIC chip has been more energy-efficient than the last, in terms of hashes/kilowatt hour). So it is easy to at least roughly quantify how much energy the bitcoin network is consuming.
On the other hand, it isn't really easy to quantify how much energy is used to uphold the traditional financial system. What do we even include in that calculation? How much digital infrastructure is required to support that system, and what does that infrastructure cost to run and maintain? How many humans are diverting their skills and attention to building and maintaining that system? Should we include the energy expenditure of things like the US military, when considering the ongoing security of the US dollar system? There is no clear answer here.
But this helps to reframe the question: given that a large portion of the security cost to maintain the bitcoin network is very directly and efficiently used to create security (ie, it is used to compute SHA256 hashes), we might start to wonder which system is actually more efficient than the other. The relative ease of quantifying bitcoin's security costs make it look terrifyingly inefficient at first glance.. but is it really? How can we make such a proclamation, without having a good idea of what we're comparing it to?
Consider: If we have some finite amount of energy to use, would it be more efficient to use it to hash some data for security, or use it to nurture a human being, who can then spend their life working to maintain the traditional financial system? How much of that input energy is actually going to create security in each case? With proof-of-work, it is a very quantifiable, large portion of the net energy, but with a human, there is going to be a lot of inefficiency and loss! It seems to me that using that energy directly for computation is going to be more efficient - despite the obvious issues that we'll encounter when trying to exactly quantify this relationship.
At this point it is probably also worth mentioning that the cost of this security is ultimately measured in the opportunity cost of that energy. Given the above question of 'energy spent on computation vs nurturing a human', we need to consider the opportunity cost of not having this human work on other projects that could benefit society (and likewise, the opportunity cost of using the energy for something other than proof-of-work mining).
If this idea of 'quantifying the energy cost of a human' seems strange or contentious to you, realize that only furthers the point about the how hard it is to quantify the energy costs of the traditional financial system. Where do we draw the line on what costs are included? The answer to that is certainly not clear, and the validity of the entire question really does depend on it.
A few other related remarks:
Bitcoin allows for permission-less financial innovation, so we should expect to see more and more novel financial constructions created upon it in the future. Being a digital asset, friction for economic activity using it is supremely low (it is as simple as communicating data to your counterparty over the lightning network, for example), and so we can likely expect to see entirely new economies arise, as users are capable of transacting value in ways they never were before. This would allow users to better capitalize the things which they already value-- which is to say it will 'unlock' value, growing what we might call the 'GDP' of humankind. With the potential to unlock value in this way, it is interesting to revisit OPs question, as that value would not otherwise be realized. To put it differently: what is the opportunity cost of not seeing bitcoin enable this expansion of economy?
Over time, humanity as a whole has consumed more and more energy, and there is no reason to believe this trend will reverse. There are of course better and worse ways to consume this energy, but it seems strange to just regard all increases in energy use as 'bad'. It seems very unlikely that humanity will stop this trend of increasing energy-consumption.
A lot of content you'll find from the 'pro-bitcoin' side of this question likes to highlight how much renewable energy bitcoin is using. I think this kind of misses the point, its great to not use energy that incurs negative externalities (ie global warming, etc), but more importantly we should consider the opportunity cost of using said energy in whatever way.
This thread by @nothingmuch on the topic of mining effeciency is really interesting! To quote from it:
the payoff from consuming finality is positive sum in this regime (higher velocity of money => more subjective value created) and the cost of a 51% attack increases even if the energy consumed decreases. since mining is zero sum and is in competition with all other uses of energy, that implies that as demand increases because of a need for higher efficiency, the relative fraction of energy expended on PoW can decrease without necessarily compromising finality.
tl;dr because money has positive utility even though it has no intrinsic value, if finality of transactions with that money needs PoW then the more useful that money is, the smaller the relative share of energy must be expended on PoW for a fixed level of finality assurance.
As reply to a few of your points:
An answer should probably be based on a guess what the proof-of-work/proof-of-stake/proof-of-solvency/etc. ratio will likely be in the future. How much would a change of this ratio affect the ecological impact of cryptocurrency?
I don't believe that proof-of-stake/etc offers the same security guarantees that proof-of-work does, and thus it cannot be used to secure systems in an equivalent manner. Without these security guarantees, we cannot realize the same benefits that we can with bitcoin (proof of work), and so in my opinion it becomes an uninteresting question to compare the two. There is a lot written about the deficiencies of proof-of-stake, this article is perhaps a good starting point.
This answer has become quite long, so I'll include a TL;DR:
Bitcoin mining consumes energy to create security in a very quantifiable manner, but the legacy system is hard to quantify in the same way. Considering the efficiency of computation, we may actually conclude that the bitcoin network is a more efficient system of attaining transaction finality, but I have not provided a rigorous proof of this by any means.
So what is the 'ecological endgame'? I think it is that the bitcoin network continues to use a large amount of energy to secure the history of the network, and it enables a huge amount of new economy in doing so, thus justifying the opportunity costs of the energy expenditure.