Yes, the SIDS foundations don't recommend you use a second hand cot mattress.

However, we also got a mattress with our second hand cot and found that it was useful to have a spare eg. during emergencies such as gastro events when the usual mattress suffers an "incident" or to keep under the cot to pull out easily when you need to bunk down on the floor of bubs bedroom for those difficult nights. It has also been useful to put next to the toddler bed too if bubs falls out of bed. Another handy use is for visiting toddlers to sleep on as a spare bed.