Suspension importance on firewood trailer

Not really... The suspension smooths out the bumps in the road so the load doesn't bounce as much.

If your suspension is worn or you have overloaded (mis-loaded) the trailer you'll see the trailer bouncing up and down and if the road is uneven the trailer can also jump side to side. Both of which are risky either the trailer can come unhitched or sideswipe a passing car! You can also encounter tires going flat from the bouncing as well as uneven wear.

The only place you could get away with this would be on your property and going real slow!