Nothing so deep as that needed here to understand what is going on; it's a paid vs free issue - free versions are less competent while paid versions of the reasoning/thinking models are getting it right. Different providers may hobble their free versions less, so those ones also get it right.

The guardrails you have outlined will help squeeze out more performance from smaller/less capable models, but you shouldn't have to jump through these hoops as a general user when clearly better models exist.