Cassettes are a pain. Head alignment is extremely important for analog tape fidelity, and it's always off for home recordings.
With pro analog tape recordings (e.g. 2-inch 24 track, half-inch 2-track), you record alignment tones onto the tapes to capture the state of the recording device, and then later calibrate the playback device to the particular tape so that playback alignment matches recording alignment. But this is essentially never done with cassettes, so you have to earball it.
Cassette players for mastering studios actually have alignment options (e.g. adjustable azimuth) that aren't present on consumer devices. But without the tones, you have to guess.
The problem with starting from a digitized source is that it may have been digitized from non-aligned playback. Ideally you want to go back to the analog originals - but old cassettes are rarely in perfect condition.
Interestingly, the Nakamichi Dragon is/was a cassette deck that can do automatic azimuth adjustment on playback -- without having recorded tones to work with.
In loose terms: It does this with a special read head that splits one of the recorded tracks into 2 distinct signals (for a total of 3 signals from 1 stereo recording). The split tracks' signals are compared, and it adjusts the azimuth (by minutely rotating the head) until the signals from the split track match most-perfectly.
A better overview is found in this sales flyer: https://www.richardhess.com/manuals/Nakamichi/dragon_folder....
(Take note of the pictures of the machine. If anyone finds one sitting around at a flea market or in a forgotten pile of old junk, please rescue it. Nothing like this will ever be manufactured again. Even if the condition is "it looks like someone went after it with a big hammer as part of their anger management process," the bits that remain still have significant value and are easy to sell.)
I don't miss cassettes one bit, but I really miss marketing literature that reads like that. A masterpiece in itself.