As greening measures go RECs tend to be one of the better options since they guarantee that for each certificate a given amount of renewable electricity is generated, so if that's what you want they work perfectly.
If a power retailer wants to sell "green power", for example, this is a simple mechanism to do that. The electricity supply is a common pool - all the generators feed "the grid", the customers draw from "the grid" (which is a local thing for a sometimes international value of "local", but there is not a single world-wide grid). So your "green power" is just normal grid power, but the retailer buys RECs to cover the green power they sell. So the renewable generator gets a price premium for (at least some of) the electricity they generate, and the customer is assured that the price premium they pay actually goes to renewable generators.
The problem is that "greening industry" is essentially unrelated to the question of electricity supply. RECs work to green the electricity supply, no more. But for most industries electricity is a small part of their costs, and those emissions form a small part of their pollution. For example the coal-fired steel refinery is going to be almost completely unaffected, since its major emissions are from thermal heating using coal. At the other extreme, for an office building electricity makes up a small portion of the rent, and salary costs normally dominate that by a huge margin. Halving or doubling the electricity cost won't much affect the cost of running a business in the building.
RECs are often introduced as the measurement device for a renewable electricity requirement, and the latter is where the major benefit comes from - few people with buy RECs just to have RECs. But when legislation requires that some percentage the electricity supply has to be renewable and measures that using RECs, RECs work very well.
There is usually a small secondary effect where the cost of electricity goes up because historically renewable electricity has been more expensive to the consumer than fossil electricity. This makes investment in efficiency more attractive and hence lowered demand slightly. But that is a small effect, and most consumers will not invest in efficiency just to save money (this includes businesses who consume electricity). It's also an effect that is local (some countries already have either all or no renewable electricity) and reducing over time as the cost of building renewable generators drops.
Note that in Australia when the government wanted to boost the take-up of residential solar, rather than increase the payment directly they instead issued more RECs per unit of installed solar (thermal hot water or PV). So now there are "large scale RECs" and "small scale RECs". The latter being worth a fraction as much as the former, as well as being worth less because they were based on an estimate of lifetime output rather than actual output (the renewable energy requirement specifies that only a small portion can come from residential RECs). This is a classic case of politicians making a mess of a simple concept for arguable short-term political benefit. But it's what Australia has.