Why is it important that the steerer tube is cut straight?

The rougher/coarser your saw, there is more chance of fraying the steerer tube too, the guide stem helps from this perspective as you finish the cut. Or insulation tape. I've had steerers where a whole shard has split off over an inch down the steerer when I havent used tape or a stem to hold it together 😬

I use an old stem clamped on to the steerer as a guide. Doesn't have to be factory square, I've had it a few mm off over the years and it's fine - so long as you can still preload the headset. Once cut and fitted, a 5mm spacer above the stem usually helps with the gap needed between steerer and top cap too if the cut is a bit wonky.

Don't forget to seal the top of a carbon tube with superglue!

Basically the less square the cut, the less leeway you have for preloading the bearings. Tightening the top cap pulls the steerer tube up towards the cap, which puts pressure on the bearings. Say you have a standard 5mm spacer on top of your stem - if you cut the steerer a few mm off square then you're more likely to top out the steerer when it pulls up, thus be unable to tighten and not put enough pressure on the bearings.

A precise 1mm extra all round the top of the stem to sit the spacer on gives you 4mm of tightening potential. Every mm off square reduces this potential

I wrap masking tape around the tube and cut to the edge with a regular hacksaw, and tidy up with fine sandpaper.

With an alloy steerer, I use a plumbers pipe slice which gives a nice easy clean cut. 

No, it doesn't have to perfectly square but it has to be reasonably square. More importantly, you don't want to cut too much off and I would be more confident of that with a hacksaw and guide than with a rotary saw. And it isn't exactly the most time-consuming of jobs, anyway.