Can you get cheaper insurance with more experience?
It's not at all clear that more total flight hours correlates to lower risk. Data shows that pilots with &lt;200 hours of total flight time are at the lowest risk of having a serious accident. 

One can speculate the reasons for this, but the truth is, aviation accidents are still very rare occurrences. This makes gathering and analyzing data difficult. The data is very noisy due to the low sampling rate. 

That said, statistical data points to a low rate of accidents until somewhere between 100 and 250 hours. Then it increases steeply, reaching its highest point around 500 hours for non-instrument rated pilots, and 800 hours for IR.


Annualized non-IR GA accident rates (median TFH=250.5)*


Figure 11. Annualized IR GA accident rates (median TFH=823.5)*

Statistics have long shown a "hump" in accident rates at the middle zone of experience. 

From there it descends slowly over time but never reaches the low rates of new pilots. Another thing that occurs is that the number of pilots at a particular level of experience decreases extremely rapidly after a few hundred hours. It decreases to the point where the number of pilots with high hours is very small. The sample rate is then so small that it's close to impossible to come up with an accurate risk assessment. 

Additionally, sometimes insurance rates are obviously driven by factors other than risk. Most aircraft insurance will give a discount for instrument rating. But if you look at the above graphs, IR pilots are at a higher risk than non-IR. They can fly in IMC, which is higher risk, but they have cheaper insurance. This is clearly a marketing decision. If one insurer gives you that discount where others don't it will attract more customers. 

* Source: Predicting Accident Rates From General Aviation Pilot Total Flight Hours,William R. Knecht
Civil Aerospace Medical Institute, Federal Aviation Administration