That depends on the privacy protections where you live and the policies of each service:

• most places in the US - they already have your data and aren't obligated to delete it
• outside the EU - probably the same as the US
• the EU or select states (e.g. CA) - you have some protections and a legal obligation to honor delete requests

For the first two, I wouldn't bother. I personally poisoned my data with Reddit before leaving, because I've heard of then reversing deletions. For the third, deleting may make sense.

But in general, I'd keep your other accounts open until you fully transition to the new one.

Below is information when considering a replacement service.

Anything where data is stored on a server you don't directly control can be leaked or subpoenad from the org that owns that server. Any unencrypted communication can be intercepted, and any regular encryption (HTTPS) can be logged by that server (e.g. under court order without notifying the customer).

Even "secure" services can be ordered to keep logs. Here's an example from Proton mai, and here's one involving Tutanota.

So it depends on your threat model, or in other words, who you're trying to keep away from your data. Just think about how screwed you might be if:

• a hacker dumps the servers data
• a police agency secretly orders recording of data and metadata
• someone steals your device
• the police confiscate your device

The answers to the above should help you decide which to type of service you'd feel comfortable with, and what tradeoffs you're willing to make.