If the collet noses do not clamp the hex rod tightly enough, it may indeed be that the noses are cracked or worn. This really only happens to the cast noses that came along in 1971 or so: these later noses are not usually found on earlier drums.
But, sometimes there is a 'generational' mismatch between the tom arm and the collet plates on the drums. The earlier arms used a fractionally small hex stock and often can be difficult to tighten properly in later collet plates. Conversely, many times a later tom arm will not fit into an earlier collet plate.
In either case, new collet noses won't help.
The collet plates in your photos look like later units, so if you do buy Rogers toms arms, better they are 'later' rather than 'earlier' examples.
I really hate to admit it, but those Yammie ball/socket joints do look good. Too bad they don't have a hex shaft on the bottom that would fit into the collet plate on a bass drum. For heavy gigging, it would be a setup I could 'live with.