Does in-the-field experience suggest that a HTTP POST is more reliable than PUT and DELETE

Question

I need to cross reference my experience with that of professionals, as I'm developing a REST application that can either

• Use on HTTP POST for all delete and create operations
• Or use HTTP DELETE and PUT for the same operations

Is there any evidence to support that HTTP POST has a more consistent behavior w.r.t caching proxies, forwarders, and even Tor.

I suspect that that by using more methods than just POST, there is an increased risk of bugs int he following areas:

• Sticky caches that have unexpected behavior with Cache-Control
• Possible implementation inconsistencies with same origin policy
• Compatibility with network inspection and analysis tools
• Alternate encodings other than application/json (I may want to use Protobuf or a binary stream for efficiency)
• ...?