The recipient doesn't necessarily know ahead of time how profitable the investment will be. Risk aversion will cause them to avoid investments that are profitable in expectation if they believe the chance of ending up worse off is too high. By offering interest-free loans, the government can pool that risk so that individual loan recipients hesitate less to make the positive-expectation investment.

Well...

>>> If it has a $100/mo loan payment and saves $150/mo on the electric bill then you take out a loan or buy it on an installment plan and don't need to have any accumulated capital in order to do it.

This depends on whether you'll pay back the loan. Just because paying the loan back saves you $50 / month forever starting immediately doesn't mean you'll do it. You might be the kind of person who takes out a loan, spends all your money on something else, and lets the bills go unpaid.

If you aren't that kind of person, you probably do have some accumulated capital.

But if you are, just the fact that the loan is hugely profitable and you should be able to pay it back - if you were a completely different person - doesn't mean you'll be able to get the loan. You shouldn't be able to get the loan, because you won't pay it back.