Firstly, transaction fees are not part of the subsidy, they are part of the block reward. You have your terms mixed up.

The subsidy is initial distribution of Bitcoin. Inflationary monetary policy The fees are payment for services

Both make up the block reward

Secondly, I am not that worried. Peter Todd who does Bitcoin core testing and things, is worried and you can read that here:

In which he references this paper: https://www.cs.princeton.edu/~arvindn/publications/mining_CCS.pdf