The Enterprise is a huge ship. Some incredibly deadly gases, emissions, etc. are on board the ship at all times in respective areas safely stored and monitored of course.

After the second battle with Khan, Mr. Scott tells Admiral Kirk that he's had to take the mains offline due to radiation.

Khan starts the Genesis device and the Enterprise can barely limp away from Reliant due to warp drive being offline.

Mr. Spock overhears this and takes it upon himself to repair the damage dying as a result. Needs of the many... Blah, blah, blah...

Did no engineer think to bring a HAZMAT suit or two?

I don't buy the answers "It was a training mission and they had no time to bring any." Or "The radiation was far too deadly even for the best HAZMATs." Or even, "All the engineers were killed during the two space battles." Or "Spock is only half human and thought he could tolerate more radiation."