So let's start with what the IO actually is, and the intended use case.
A very small amplifier with a 30w/8R rating, no 4R rating and occupying about half the volume of an old shoebox Nait, or Cyrus. Unless you've handled an IO you won't appreciate just how petite this amp actually is.
It is designed for use with small loudspeakers of limited LF bandwidth and a relatively benign loading, with MM vinyl as the primary source.
First let's look at the heat issue. Case sides reaching 45deg after 20+ minutes of sustained drive with test tones is not unusual. Go pull out an old Quad 405 (100w/8R) or Cyrus amplifier and try the same trick - you'll get a similar result. Moreover, 45 degrees is not 'burning hot'. Perhaps the reviewer has particularly sensitive hands.
In addition, this amplifier along with all Rega designs runs with higher than typical bias current - part of the design philosophy - if it ran cool it would be faulty. All Rega amplifiers contain thermal protection and will shut down if the output devices exceed a fixed point, which from my own testing is when the sinks/case gets to the mid 50 degrees.
Distortion and noise. Better than 0.05% and so not audible in the vast majority of use cases.
Distortion+noise appears to rise with output into 4R loads. It sure does - but look at the expanded scale - 1dB variance in the plot!
Utterly insignificant.
Crosstalk. The reviewer is fixating on the worst case figure of 30dB, which is at 20Khz where crosstalk will be inaudible.
At frequencies where this matters most it sits around -45dB. Not great but a function of cramming so much into a small case and likely capacitive leakage across cramped PCB tracks, but again it isn't high enough to impact soundstage and imaging. If it were, you'd never ever run a phono cartridge!
Phono RIAA and overall response.
It's largely flat but rolls down a little at the very top and bottom. An eminently sensible design choice for a budget amplifier of limited power destined for use with smaller loudspeakers. Extending LF response unnecessarily on the phono input with a small amplifier is asking for trouble. Rega sensibly avoid this pitfall. To be clear, the response is a paltry 0.75dB down at the audible extremes.
Dynamic or burst power is roughly double that of the RMS capability. This means that for a small amplifier the design focus has been placed squarely on performance under dynamic condition, I.e. music and not lab signals. Again, sensible design choices by Rega.
High headphone output impedance.
Yes, fair point, but typical for amplifiers which drive headphones by padding down the main output. It's a nice to have facility but no substitute for a dedicated headphone amp. I don't believe Rega claim otherwise.
You cannot have everything for £379, and certainly not for a UK built product.
Rega compromised wisely to suit the budget and intended use case.