Most policies today cover Covid as any other illness. In that case, purchase of the policy is not time sensitive.
You do have to be mindful of time windows if you want a waiver for pre-existing conditions. Celebrity coverage is a bit different because its cancellation fee waiver is provided by the cruise line and is not part of the insurance underwritten by Arch. It does not cover a condition that is diagnosed or treated in the sixty days prior to purchase, but it allows you to cancel for any reason with 90% FCC.
On the other hand, third-party policies require you to purchase within a window related to initial deposit in most cases in order to qualify for a wavier of the pre-existing conditions exclusion.
There are some policies such as IMG LX that will allow the waiver if purchased at final payment. The advantage is that you do not have to buy the policy until your money is at risk, assuming you have a refundable deposit. One purchased, insurance is not refundable beyond the initial inspection period, but it may be transferrable to another cruise.
The key is in understanding what a pre-existing condition is. Without the waiver, something as simple as a change in RX, a reported symptom, or a diagnostic test occurring in the look-back period can result in a claim denial if it can be tied to the reason for cancellation.