the rate of transactions in the system is directly tied to its mining rate
How so? That's not my understanding at all - you could have a rate of transaction at the level of VISA with just a dozen computers or so. The mining difficulty is a consequence of having many miners (which makes the software auto-increase the difficulty of the problem), not of the increased transaction rate.
the block rewards will become rarer and rare till they eventually halt
That's why there are transaction fees, which pay the miners in lieu of the block rewards.
It's an ouroboros turning into a catch 22 you can't have an open system with high level of trust if the computation is trivial.
Ever increasing difficulty raises the bar so high that it centralizes a system due to the hardware requirements (there is no way to effectively mine BC today on standard computing hardware sorry) and their costs.
Look at the BC network now it's either huge centrally controlled mining pools or multi-million dollar mining farms which are controlled by individuals, this isn't decentralization of anything but computing assets as far the the pools are concerned.
How so? That's not my understanding at all - you could have a rate of transaction at the level of VISA with just a dozen computers or so. The mining difficulty is a consequence of having many miners (which makes the software auto-increase the difficulty of the problem), not of the increased transaction rate.
the block rewards will become rarer and rare till they eventually halt
That's why there are transaction fees, which pay the miners in lieu of the block rewards.