Are modern coal plants really all that harmful to the environment?
Yes. Perhaps you've heard of climate change?
I thought they were able to capture the emissions at these big plants.
The cost of carbon capture for coal plants makes the operation far more expensive (per MWh and per MW) than nuclear or renewables. As a result, a tiny fraction of one percent of coal-fired generators in first world nations are capturing the carbon emissions and sequestering them.
As for your second paragraph -- it's one thing to be ignorant of a specific industry and its technologies and economics. That's your first paragraph, and that's fine. That's how we learn. But the ignorance exhibited in your second paragraph indicates a different kind of ignorance altogether. Please go back to the kiddie table.