This news seems to hint that Harry Kane will leave this summer and especially if for family reasons it means he is serious about leaving Spurs. I think it is true that now is the right time for Spurs to let go of Harry Kane for the two reasons that you said will actually hurt Spurs in the coming season.
Except if Tottenham want to lose him as a free agent, its better they let him go now while there is an offer and they can reinstate a new striker that can replace Kane, they shouldn't wait until summertime because even the potential buyers would want to have him as free agent, they can settle less for Bayern or face what Mbape is facing with PSG now looking for buyers up and down and I'm very sure that Kane wouldn't go to Saudi Arabia anytime soon.
Meanwhile, Bayern Munich are currently offering too much for Harry Kane and they are very serious about being able to secure his services before the transfer window closes. Maybe the Spurs owner should be able to cool down his head and be more willing to let Harry Kane join Bayern Munich so that at least his flagship player can feel the title he has long dreamed of.
Is it that hard for Bayern to make a decision to remit $100k for Tottenham, maybe there is something they have secretly in mind they are not telling us otherwise this deal ought to have been completed by now even with Mane or without him, they have the financial power to buy Kane without feeling down from their bank; it will be a great deal for them and Tuchel will have enough options to utilize in matches since he is always complaining of competition among players, having a favourite will reduced that in my opinion.
One thing about Bayern Munich is that unlike the other European giants, they hardly spend hugely in signing of footballers. They would always want to spend less on big players they are very certain that will deliver exceptionally when they arrive the club.
With how public their offer to Tottenham to sign the England national team captain is, they're supposed to finalise that deal by now and let Thomas Tuchel do his best and bring the best from the Tottenham striker