It wouldn’t be “necessary” at your weight but it may still be a preference. There is more about the effect of thicker mattresses in post #14 here.
There are really only two ways to choose a mattress that is a good match for you in terms of PPP (Posture and alignment, Pressure relief, and Personal preferences).
The first is your own personal testing or experience on the same or a very similar mattress.
If you can’t test a particular mattress or a mattress that has a very similar design in person before making a purchase … then the second would be a more detailed phone conversation with SleepEZ. They will know more about “matching” their mattresses and the options they have to different body types, sleeping positions, and preferences than anyone else (they do this every day) and can help “talk you through” the choices that have the best chance of success (see mattress firmness/comfort levels in post #2 here).
It would depend to some degree on the construction and strength of the foundation and the amount of sagging it allows (some wood and types of construction are stronger than others) and whether it has good center support to the floor underneath it but I would say “probably yes” it would be fine and it will also even out the support surface enough that it would likely be OK with sagging in between the slats as well.
I would tend to choose a support surface that allowed for better airflow under the mattress (see post #10 here).
Another alternative would be a slat conversion like this which would be more rigid yet and also allows for airflow under the mattress. Pegboard would also allow for more airflow under the mattress than a sheet of plywood.