The streaming business model -- from the artist's POV -- is that a tiny royalty is paid *per streaming instance*, i.e., if a track is streamed once, the royalty amount is paid once, if it's streamed twice, the royalty is paid twice, etc.. Prseumably Spotify Premium -- which allows you to capture a playlist so that it can be played offline, but does NOT allow you to transfer that content to another device -- has some way of keeping track of how many times you've listened to offline content, so they can adhere to the required royalty structure. (I say "presumably" because I haven't heard of any major lawsuits alleging that artists are being cheated out of royalties by streaming services that allow offline listening.)
If you capture the streamed content in a way that allows you to listen to it outside of the Spotify app (including transferring it to another device), so it's neither streamed nor counted, subsequent royalties aren't paid because the content isn't being streamed repeatedly. It doesn't matter if you keep your account active: if you don't stream, the artist doesn't get any payment.
Your method, of buying the stuff you really like, is much more ethical, and in the long run better for everyone, including you.
As far as I can tell from the Spotify license agreement, you don't "own" streaming or offline content: copying the content out of the app and keeping it is probably a violation of the agreement, even if your account is still active, and certainly if you close the account.
Sidify, like many other computer applications that claim to circumvent DRM, is almost certainly just capturing the streamed music as it plays, and then re-encoding it to whatever format you've chosen. The marketing claims of "lossless conversion" on their website are what I call weasel-speak. If you can play it, you can capture it -- that doesn't make it lossless.
Cheers -- The Grinch :)