Every time I've been exposed to the operational aspects of a government agency (and, unfortunately, most large non-profits and even some large corporations) I see things being done in a way that costs around five times as much as we would do it in small- to mid-scale private industry, and even at that expense level the quality of work is outright appalling. When you start working with the management of these organizations, they simply don't care about setting appropriate standards for what they can achieve on a certain budget and then squeezing things to make do with what they have. Quite the contrary, their incentives are structured around having as much budget as possible. So bloat is everywhere, and the response to any additional "needs" is to demand more money. This is an endless cycle - giving them more money will never achieve their goals, because that would harm management's careers.
Privatizing these functions is its own can of worms - it's often far cheaper (see: SpaceX vs. NASA), but still a long way away from excellent, and rife with corruption and politics (see: Military-Industrial Complex, Prison-Industrail Complex, etc).
If I really wanted to have the EPA catch these things the best method I can think of would be to offer bounties paid on caught cheaters. This creates incentives to check everything everywhere, and retains the incentives to maximize efficiency.