In most cases buying early will also cover you for new medical diagnoses and conditions that occur after the policy is bought (but not if you are still waiting for tests or their results at the time of purchase). This needs to be checked thoroughly in the full policy Ts&Cs before purchase to see what applies. Some insurers will cover regardless; some will only cover if not diagnosed by the date of departure; some will not cover at all unless separately notified and potentially repriced after the policy has been purchased but before the date of departure. It's a minefield.
It's an hour or more of your life you'll never get back reading policy documents but never assume you have cover for something on insurance unless you see it written down in black and white. If in doubt it's best to find a local in-person insurance broker to do all of the work for you.
Example: A colleague at work had a heart attack in New York in 2017. The medical costs came to nearly £1m after the open heart surgery emergency operations he had to have plus all of the aftercare costs of being stuck in the US for three months before he was fit to fly home. Because his policy accidentally excluded the US from an otherwise Worldwide policy (because the US are known to be very expensive for medical care so it costs more in the premium to cover US trips), he wasn't covered. He had no money to pay for that bill so the hospital sued him in the UK courts and he was made bankrupt and he lost his mortgage-free fully-owned home and all of his assets. He also lost his entire Defined Contribution pension as he was over 55 and they went after that as well - because it's accessible from age 55 onwards so is a cash asset that can be liquidated (unlike Defined Benefit pensions which can't be touched until retirement as they are not liquid assets). He is now living in a housing association flat having to start his life again from scratch with less than 10 years until retirement where all he will get is the State Pension plus what little he can save privately in the next few years. Horribly sobering story of what can happen if underinsured or not insured.
I today bought my policy for an upcoming Just You China trip in October. I searched using a comparison website and the cheapest was £40. I bought the third most expensive policy in the list instead at £118 because it had the highest coverage levels and the least number of exclusions. You get what you pay for with insurance policies! I also then bought it directly via a cashback website so the 18% of cashback was paid to me and not to the comparison website.
Examples of extras I have made sure are covered include; very high coverage limits in all areas; no exemptions for drone disruption at an airport (I flew out of Gatwick on the Just You Marrakech Christmas trip the day after December's drone closures and only just got out before they closed the airspace again); no exemptions for scheduled airline failure; no exemptions for supplier (Just You) failure. Some of this is of course covered by the ATOL/ABTA protection, as well as on Section 75 credit card protection - but only the holiday costs. None of the peripheral costs are covered otherwise such as transport to/from the airport; overnight stay at an airport before/after the holiday; fees for kenneling you have paid out etc. You need extra cover for those bits to be claimable.