I carry hull insurance and as most folks know, the rates go down at something like 250, 500, 1000 PIC hours, if you have an instrument rating, etc.
If all you carry is liability insurance, and/or your total time and/or time in type is a 4 or 5 digit number there aren't any more price breaks you can get.
But every log tells a story. Perhaps when I am old and can no longer get out of my rocking chair someone can read me my pilot log and remind me that I was young once and bold...
Best of luck,
Wes