This is a good middle ground, but ...
... leakage by timing side-channels depends in parts on how accurate your time-measurements are (e.g. Javascript's timer resolution was degraded, in order to make transient failure attacks like Spectre harder [1]).
I totally agree with your second point and believe, but cannot prove, that no current processor with any competitive performance is free from timing side-channels, the best we can currently do is put upper bounds on leakage rate. There are just so many other timing side channels, e.g. port contention [2]. They just keep popping up ...
Another dimension is the very meaning of thread. Presumably, as an end-user, you care about the threads/processes that the operating systems defines. But they don't map one-to-one to hardware threads, cores etc. Indeed I would argue that processors don't have threads in the sense that end-users care about. So the relevant security property must be regarding a hardware/software interface. Quite how to nail down this isolation property is active research I think. See e.g. [3] for work from 2016 in this direction.
Yet another dimension to this is through passwords and similar mechanisms: presumably you want to allow doing things like "sudo" so a low-priority thread can increase priority, provided the former knows the right password. But the very act of supplying a false password, leaks a tiny bit of information (that can be quantified in terms of Shannon-style information theory) about the password's search space.
[1] https://hackaday.com/2018/01/06/lowering-javascript-timer-re...
[2] A. Bhattacharyya, A. Sandulescu, M. Neugschwandtner, A. Sorniotti, B. Falsafi, M. Payer, A. Kurmus, SMoTherSpectre: Exploiting Speculative Execution through Port Contention. https://arxiv.org/abs/1903.01843
[3] D. Costanzo, Z. Shao, R. Gu, End-to-end verification of information flow security for C and assembly programs. https://6826.csail.mit.edu/2019/papers/certikos-sec.pdf