Google ranks Local Services Ads through an auction. Two of the things it weighs are your bid and how likely your ad is to turn into a real lead, and that second part is where response speed comes in.
In Google's own words, one of the ranking factors is "your responsiveness to customer inquiries and requests," and "missed calls may negatively affect your responsiveness." Your average response time also feeds your profile quality, and Google says higher-quality profiles "may rank higher and may also pay lower costs per lead."
So answering faster isn't just good manners. On LSA it can lift where you show up and lower what you pay for each lead, while slow answers and missed calls push the other way.
Source: Google Local Services Help, About ad rankings.