In many cases the risks of trying new things, applying for grants, or otherwise putting yourself out there, are miniscule. But the gains can be enormous. The main risk of applying to a prestigious fellowship is that the time invested in the process would be better spent elsewhere. I've certainly felt at times that I was spending too much time chasing money to do my research and not enough time doing it. Other than that, there is not much of a downside. Send an article to a journal that you think might reject it, you waste time that would otherwise go to having it considered somewhere more realistic. You could also risk the disappointment that comes with rejection. However, the pay-off could be very great indeed. If the likelihood of success is even 10%, it might be a good gamble, if it does not entail a huge amount of work.
I used to just always have a grant proposal. Whenever something came up, I would modify that proposal for the requirements of that competition.