This is not a resource problem. The danger of the incentive that mandatory minimum sentences create affects every accused person when they're engaging in a cost-benefit analysis of what to do: Do I take a matter to trial because I am not guilty of the offence, or do I just resolve the matter in some way so I don't risk having to go to jail for a mandatory period of time?
The problem becomes exacerbated among accused people who belong to certain communities, because members of those communities, as a result of issues with poverty, may not have adequate supports or resources or advice to make those types of decisions, so it is not uniquely a problem of resources; it is a problem that mandatory minimum sentences create for all accused, namely the incentive to plead guilty to a different offence.