I don't think both the problems ever gonna solved. As far as problem one is concerned, it is impossible to ensure equitable distribution of cryptocurrencies since at the time of entrance not everyone knows the potential of coin and almost all the cryptocurrencies have very less population as initial investors which means large individual holdings. As coin gets popularity and surge with time, more people start buying that coin but they can only own low supply since price is high. So initial HODLers with large supply will always be present for every coin.
About problem two, speculation can never end for Bitcoin or any other coin since cryptocurrencies are majorly used as trading investment and items of trading are always subject to speculation.