Why is timestamping important in Bitcoin?

Could you elaborate on the significance of timestamping in Bitcoin? How does it contribute to the overall security and integrity of the network? Are there any specific mechanisms employed by Bitcoin to ensure accurate and tamper-proof timestamps? Also, how does timestamping help in preventing double-spending and maintaining the order of transactions within blocks? Lastly, are there any potential vulnerabilities or limitations associated with timestamping in Bitcoin that investors and users should be aware of?