As someone who has been a non-dom in the UK, I have some pretty mixed feelings about it.
Basically, the way it works is that you can claim non-dom status for a certain number of years (15, I think). You pay a flat fee for the first 12 years of around £30,000 and then £60,000 for the last three. You then pay whatever tax rate you fall into on any money you remit (bring into the UK). So most non-doms keep as much of their holdings as possible, either offshore (the Channel Islands basically exist to facilitate this) or in their native country, and bring in as little as possible. Although fun fact: money you bring onshore to pay tax is considered a remittance and will be taxed in the next year.
Our tax rate here is 45%, our tax rate in the US is (I believe) 37%, I do not know the rate in India, where I think Akshata Murthy is domiciled. Weirdly, we also have a substantial tax bill every year in California, despite not having set foot in the state for so much as a weekend in probably twenty years, as they take a portion of income generated from any business there. There are also some complicated deadlines where if you pay a certain amount by a certain date in one country or the other you get a small credit against your liability in the other.
Even in our case, and we're worth much less than she/they are, it requires a lot of hours by knowledgeable accountants. IMO, it really is not like getting tax relief on a pension or ISA, which is pretty straightforward.
I actually think it's a pretty crap policy, and it's not a great look for the family of the man in charge of monetary policy to be taking advantage of it, but it is legal. I find it particularly troubling as there is talk of abolishing it as a policy and he was hardly in an unconflicted position. We converted to domiciled earlier than we needed to as we had some moral queasiness about the bulk of our tax money not going to support the place in which we were living and raising our family, but I suppose, while not an insignificant amount, we had less to lose than they did.
Last thing - I've seen a lot about how it's her money and sexism etc. to expect her to accommodate his career. I don't know their setup, but my husband and I have both worked in an industry where there are certain investments we would not be allowed to make because it would raise a conflict of interest, so I'd be surprised if they'd never run across that issue.