but not the privacy problems? Did I overlook something here?
Yes, unfortunately. When you later spend you often need to use coins originating from multiple transactions that previously paid you and these co-spends will link together your transactions.
For example. Say Alice pays you 1 bitcoin to address A and then Bob pays you 1 bitcoin to addess B. You then spend 2 bitcoin and use those to coins, indicating to the world that the same party probably controls A and B. Later Bob pays you 1 bitcoin again and Charlie pays you 1 bitcoin to address C. You make another 2 BTC payment using the coins from Bob's second payment and Charlie's payment, now the world has reason to believe A, B, and C are all controlled by the same party. Without the reuse people would know less.
This privacy loss doesn't just hurt you, but also A, B, and C and potentially the people they interact with so even if privacy isn't very important to you today it's still better to not gratuitously lose privacy.
Bitcoin Core has some logic to try to spend all payments to the same address at once (though in 0.17 it isn't enabled by default) but even that won't help you if the payments/spending are spread out over time. If you are forced to reuse addresses it's preferable to delay spending payments to a particular address until its unlikely to get any more and to then spend them all at once.
Using one address per paying party is the bare minimum needed to even know who paid you but doesn't provide particularly great privacy.
so you would have 1 address per user, that sends you Satoshis. This is address re-usage, and has the same PRIVACY implications, as if you'd have only one address for all users. Just at a different scale. Not sure, what the security issue is, what you mean by that. To avoid this, you may want to look into BIP32/44 wallets (HD wallets), that can assign everytime changing adresses, without you to worry too much... I put the answer here:
https://bitcoin.stackexchange.com/questions/46718/bitcoin-system-with-payins-and-payouts-using-bip32/52900#52900
The security problem is that when you create a transaction you have to publish the public key belonging to your address.
But you transact with everybody over another pseudonymity. I am sure the privacy is improved because not everyone of your transaction partners can see your balance. (for example) But I am not sure what exactly I am overlooking. – Martin – 2017-04-27T20:38:24.593