The freerider problem: Delegates can use the money for everybody (dividends, marketing, build the ecosystem) or they can pay it back to the voters. Shareholders can maximize their gains if they voted for the latter and everyone else would vote for the first.
Can you further elaborate on this? It might be obvious and it is very late and I am going to sleep but I think this discussion is important in order to avoid what you have described.
From the perspective of the individual shareholder that tries to maximize his benefit, the best (of all options) would be if (1) he approved as many delegates that give part or all of the delegate reward back as possible but (2) no other shareholder would act this way. Because then our shareholder has the best of two worlds: A stable and decentralized network which he profits from through a stable share price / an appreciation in share value. And he also has gotten the pay back from the "pay back delegates".
This is a freerider PROBLEM though because if everyone followed this rationale then the network would not be centralized anymore because shareholders would give all their votes to the one admin/provider of several delegates that pays back the most (in the long run this ends up being one delegate because of economies of scale if he needs to be profitable) or worse that is a bad actor that doesnt have to be profitable.
Freerider problems exist with all social interaction. And there are a few means to handle it (the below only partly applies to the specific problem above):
1) A centralized entity (state) that sets rules (forbidding behavior that endangers the common good). We all know the problems...
2) A "social ban" ~ traditions, cultural learned behavior that forbids behavior that endangers the common good. Difficult if the group gets to big and depends on the culture; no possibility to "hard code it".
3) Privatization: Doesn't really apply here. With other free rider problems (land or water resource used by everyone) privatization means to give the resource (that in many cases was not owned by anyone before; it has been a public good) to a private person or company. The private person/company then has an incentive to handle the resource with care. Disadvantage: Pressure of short term profit extraction (nowadays; financial markets...). And who should you give the resource to if it never was owned by anyONE?
4) Technical means. Then is is not a freerider problem anymore.
5) Love / Acting for a higher goal. Then there is no freerider problem either because the assumption (maximizing own (material) benefit) is not fulfilled.
Would it be technically possible to evade "pay back delegates"?
....I assume though that shareholders have enough collective intelligence to not vote for pay back delegates ("social ban").
Compared to POW there is less of a pressure to make a profit from pay back delegates. Miners have invested in their mining equipement and they are under pressure to make a profit from it. Also miners have not stake in the network, they don't care about the bitcoin price, with any POS shareholder who also directly or indirectly secure the network this is different.