Define 'too soon'.
It is not possible to eradicate the virus through lockdown, we are just trying to prevent the number of people needing the NHS at once overwhelming our medical resources, ie, to spread out the number of sufferers at a time.
The longer the lockdown the greater the damage to the economy on which we all depend, which finances the NHS. It's not really possible to measure how many deaths could result from that.
There are signs that the lockdown itself is causing harm, probably deaths, from people not calling for medical help for other problems, from pausing treatment programs, from domestic violence, from suicide etc, which will get worse under longer lockdown and may be greater than the harm that the Covid causes.
The only way to more-or-less eradicate Covid is a vaccination, and there is little suggestion that one will be generally available within a year. In the meantime we are going to have to accept that more and more people will catch it, hoping that a) the NHS will be able to deal with the numbers needing care at any point, b) sufficient people will develop long-enough-lasting immunity to dampen the outbreak down and, of course, c) that it will mutate and become mild or harmless.
There is the chance that it will mutate and become even more virulent, but I don't think that is thought to be particularly likely.
Until a vaccine is generally available we will just have to live with it, just as we live with seasonal 'flu, specially in the years when the vaccine isn't very helpful. Numbers aren't kept but it's thought that about 15,000 - 17,000 excess deaths per year are caused by 'normal' 'flu. I'm sure many people would want to accuse me of being heartless by saying that and say 'how would I feel if my loved ones died of Covid?' and the answer is I'd feel as awful as if they died of any other cause, which may have been the result of lockdown, and I hope we can get round the awfulness of people dying alone. But hating the prospect doesn't change the facts.
Now, hands up who would like to make the call on when we ease lockdown, how fast and in what manner ...