As someone who knows people in the energy business, I pretty much ignore how mako power plants are supposed to work because they don't make a lot of sense when compared to any type of real-world power plant. Essentially, we never hear anything about the byproducts the plants make except for the energy they produce. Instead of the byproducts being the hazardous waste, it's the fuel being burned that is, which is pretty much the opposite of how real-word power plants hazards work. In fact, we don't hear of any byproducts whatsoever which is probably a case of Failed To Do The Research on the part of the creators.
As for why there should be byproducts... All power plants (that aren't hydroelectric or wind based) work by steam power. Water is heated up by burning the fuel (or by nuclear reactions) and forced through a series of pipes to turn the dynamo that creates the actual power. The burning of the fuel itself doesn't create any usable power on it's own. It does leave behind other products that need to be disposed of, and a lot of those are hazardous in some way.
This leaves mako reactors with a bit of a problem if you're going for real-world scientifc analogies. Technically, mako is energy already and is a very usable one at that. Want more physical/mental power? Get mako in you. Or get solidified mako (materia) if you want more immediate effects. And all of that with no energy loss either. It's not like oil/coal where the energy is locked inside unless you do a bunch of chemical reactions to it. What mako isn't good for is being a source for electrical energy. From what we see in-game it's got to go through the same process that normal power-plants go though (burn fuel to make steam to turn the dynamo). I can see this happening if it's easier to get mako then to mine oil/coal or if mako doesn't leave behind any byproducts (it has a 100% energy conversion into heat). Of the two, the second possibility is pretty much the motherload of the energy industry, so I could see why Shin-Ra would have gone for that as soon as they figured out a way to convert mako into heat. No byproduct means a lot of infrastructure that doesn't have to be built. Which might also be why mako reactors can be located in such odd places.
Another other option is that mako reactors aren't so much reactors as mako refining plants. That mako isn't one substance, but is made up of a bunch of different substances and that Shin-Ra figured out how to filter all those substances out. The problem I have with this is that the different types of mako mentioned in-game usually have to do with how much the mako moves around The Planet. Chaos's mako doesn't move at all (and some of the unused text suggests the Summon's mako doesn't/didn't either) while the "main" Lifestream can move from the Northen Crater to Mideel in a matter of days. Materia is essentially mako that can't/doesn't move at all, and yet still has usable energy in it (especially if materia growth/birth isn't just a game mechanic). However, refining mako would answer where all the fuel for non-electricity power comes from for stuff like any type of vehicle and the like; some mako is formed into energy, some is formed into fuel, etc. This still leaves the problem of how mako is turned into energy up in the air though as all non-electric engines run via combustion, which again, assumes that mako behaves like all other fuel types. It also causes the problem of what fuel people use to run vehicle engines post-meteor fall. 'Cause if it's an engine that can only run on refined mako, then they're screwed. And we never see this being a problem in post-metor installments.
Then there's the part of me that says "screw real-world physics, we're in a Final Fantasy game; how do the metaphysics work?". What we do know about the Lifestream is that it's a cycle; mako is formed into lifeforms and then those lifeforms turn back into mako when they die, usually more mako then it took to create them. So as long as mako eventually gets back to the Lifestream, then there's nothing to worry about. The biggest problem with the mako reactors is that they remove mako without replacing it with more mako. Given how mako enhances humans when it interacts with them, I don't see why it couldn't enhance coal/oil the same way. That is, use oil/coal as a "container" for the mako. Shin-Ra would still be using normal power plant physics, but the mako in the oil/coal would cause the energy yields to be crazy high for way less coal/oil. If I were doing the world building, I'd probably make it something like mako causing coal/oil to effectively not convert into byproducts even while still generating heat so long as they had a constant supply of mako. That would explain why mako plants need all that mako supply without needing to rediscover coal and oil post-meteor. It was technically what was being used all along, just extremely efficiently. With no mako, new sources of coal/oil are needed.
Hopefully that'll give you some ideas. I honestly tend to prefer non-real-life science sometimes because then any errors can be attributed to the metaphysics of the setting as opposed to the creators not doing there research. Fortunately, FFVII has a lot of metaphysics to play with...
