Does the present definition of a scientist involve writing research grants and managing projects? Are there alternatives to such an approach? Doesn't exploratory science lose because of such an approach, as grants are most available only for hot research topics?

That's basically it if you want to be a PI or work in industry.

If you don't want to do that you can be a technician and just execute a project under varying levels of instructor.

Yes to your last question.

It is true for academia but this is not always true for industry.
Industry research doesn't just fund "hot topics". Companies fund what they think might result in profitable products or services or cast greater insight into how current products or services work with a view to reducing costs, increasing patents and increasing profits etc. Those are not necessarily the same thing.

Of course industry does also fund university research directly but you have a mixed bag really.

I spoke to a colleague about this a year ago. He sits on panels which make decisions on funding.
His strong advice was to avoid trying to be cautious with proposals in a misguided attempt to make it easier to secure funding.
Get a really exciting idea, build a collabarative team to deliver it and apply. Excite the funders he said. I am inclined to go with that advice.

The important thing for me is not being a scientist but instead being a research scientist. The latter is reserved for those who actively perform research activities. The former are really administrators and managers.
The term "technician" should be reserved for those doing largely routine or manual work with little or no analysis or interpretation of results.
Most academic research staff fall into the category of administrators or managers and do little or no active research work themselves. They seem quite happy to claim much of the credit though.

Of course most academic funding still goes to hot topics but there should be plenty of money for those with exciting proposals.