Rewarding consensus is completely and utterly key to the security and usability of a PoW cryptocurrency - without it, there is no way to bound transaction acceptability.
Of course, with a PoW consensus mechanism, you need rewards, to compensate for the economic loss in PoW. The problem is triple:
1) that you then get convergence because of economies of scale (see bitcoin)
2) that you waste a lot of value, in other words, your system is a net value burner. You need to waste a high amount, because that waste is your only protection. If the waste is not gigantic, anyone can attack from the outside
3) that you split the system in a set of "wasters/PoW industry" and a set of "users", and both have different objectives.
But that's more a problem of wanting to use PoW based consensus, than an inherent problem of finding consensus.
As I said, rewards give rise to strategies. Strategies can then be different than the desire to come to honest consensus. It is very difficult/impossible to find rewards such that the optimal strategy for those rewards is going to coincide with the desired other outcome, namely consensus. The systemic difficulty in reaching consensus increases if you reward the one proposing it, instead of making it easier. Normally, reaching consensus on "sufficiently old mem pool messages" shouldn't be that hard. Of course, the *current mem pool state* of all active network participants is different, because of network delays. But a list of "old enough mem pool transactions", broadcast at a certain moment by one of the participants, is easy enough to check and confirm. The "difficulty" of having several of those lists being broadcast nearly simultaneously, and arriving at different order at different network participants, can also easily be solved by including a symmetry-breaking merit function, part of the protocol, that will assign different preferences of the broadcast lists. After a reasonable network delay, most nodes can assume they received all of the list candidates, the merit function indicates which one is to be preferred, and all nodes will come to the same conclusion. That's the consensus. When the network propagates the message that consensus has been reached, nodes can start thinking of broadcasting a next consensus list, built on the previous one.
If all of this is done without reward, and just on the basis of "altruism" because one wants the system to work, there is no incentive to "game the system", to "make others accept YOUR consensus list" and so on. There's nothing at stake, apart from contributing to the good functioning of the system. From the moment you introduce rewards, it becomes strategic to be the one that gets HIS/HER consensus proposal and not your peer's one. Instead of cooperating in the network, you compete.
Such a system is totally opaque to any form of long-range roll-back attack, simply because no roll-back is possible. Reached consensus is reached consensus, done real-time and on-line. The price to pay is that verification is only on-line. If you leave the network, you trust your network peers that they continue to build the consensus.
You can think of ways to recover from the improbable "global network split", by accepting, when the network unites again, a merge consensus, that accepts all that happened on the two split histories. If you discover nodes that have another prong, with another history from a given point in time, you accept as well their transactions, as those in your prong.
A priori, these two prongs should be compatible: this is like in a DAG like coin: there can normally not be double spends of the same coin, or it would mean that there was a node, sharing both half-nets and doing double spends, one on both sides. Splitting the network is already difficult, but splitting the network and being on both at once is even harder. If ever that happens, one could accept the double spend exceptionally. That's just some extra coin creation, no problem if it is rare enough.
The important thing is that no roll-back is possible.Again, this merging is quite straight-forward if consensus DOESN'T come with reward. Because merging the prongs doesn't mess with rewards that don't exist.
In addition to that, you cannot control the value of a currency by changing the PoW difficulty. Value is derived from supply and demand, changing the difficulty only affects the supply side.
Well, if supply follows demand, price will stabilize. And supply is value-controlled: if *making* a new coin has a fixed economic cost, you will ONLY make it if its market price is higher than that cost. So as long as there IS a demand, this will converge to the set price. You are right of course that if demand simply plummets, the lowest supply (namely NO supply) cannot go lower than zero. You might introduce a systematic destruction of coins if you think that's a problem: a destroyed transaction fee, which is a given percentage of the transacted value. It would indicate a "half life of coin": grossly the number of times you can transact a coin before it is gone entirely. If you put that to, say, 1%, a coin's half life would be about 100 transactions, grossly. I don't know if such friction is a good idea, though. At least, it would make speculation impossible. You put an upper cap on value.