Surely it would be cheaper to just give those industries another grant?
Probably not, the problem with giving money to businesses is that the equity owners get it all, and then don't need to pass it on to anyone, so it just makes someone a little bit richer (whether that someone is the owner of the business or the banks etc. who are owed money by the business)
By giving money to the customers to spend, then the business has to actually provide the service - that means they have to employ the people, buy the materials etc. so the money goes straight back out and the business only gets the profit, but the employees and everyone also get a share of the money.
As to if it would be an effective thing at all, almost certainly not if it's simply funding people buying imported goods, if it's funding services then it's possibly a more effective stimulus to the economy than anything which primarily goes to equity.