Passing keys inside a TLS connection?

Question

Encryption

Hello everybody.
Purpose: to make a secure UDP connection.
In order not to write handshakes and code for transferring encryption keys (symmetric), it was decided to:
1. establish a connection via the TLS protocol; 2. exchange keys inside it; 3.break TLS connection; 4. exchange data over an already secure UDP connection using previously obtained keys.

As advantages of this approach: an already tested and stable working protocol is used, therefore the number of code where there may be a bug is reduced.

Question: what disadvantages can such a solution entail? (except for the lack of customization of the handshake moment and the key exchange embedded in TLS)

PS: by the way, in my opinion, httpsalso first uses a slow asymmetric encryption algorithm to exchange symmetric keys inside it (since asymmetric encryption is much slower than symmetric encryption, it is better to use symmetric encryption)

Answer 1

Already done.
VPN over UDP

Answer 2

That is, you are not afraid to send the key to the untrusted side? Or is the initial authentication done in some other way?