For the Cutty Sark to put to sea these days, she would have to have an engine fitted, modern lifeboats, electric pumps, GPS, radar, wireless, etc etc, all sorts of things which would detract from her as a historic vessel

How would they detract?

The engine is the main thing, of course. But engines are pretty small (compared to the size of the Cutty Sark as a whole) and don't take much room. You only need a small one for manoevring - it doesn't need to be a serious one for passage-making. Sails would continue to be the primary means of propulsion.

Lifeboats? Not necessarily - liferafts would probably be acceptable, and they pack down small.

And radar, electric pumps, GPS and radio are basically invisible to onlookers, whilst giving a modern level of safety for those onboard.

Is your argument is that if the crew today aren't experiencing the same level of danger as the original crew, then it's detracting from its "historicness"? If so, I'd have to disagree.
As Guest says, this wasn't a matter of choice - they lived (and often died) in those appalling conditions because there wasn't a better way of doing it back then. There's nothing romantic about pumping the bilges manually or running into rocks because you don't know where you are.

Graham.