Not every service can be sold online. For some, you definitely need offline service providers. Some of the examples which I can think of are the carpenters, plumbers, beauty parlor, and so on.
And they definitely cannot provide their services very far away. That means, whatever their marketing and promotional means would be, they have to be effective in their local areas only. For instance, if you are one of the locksmiths in Philadelphia, you cannot promote yourself outside of US. And in most cases, you would not be able to provide services outside Philadelphia itself.
But even then, a website would help!
No matter how local your service is, if you are a local service provider, having your own website would still help you reach out to your target audience.
Reach to a wider audience
No matter which business you are in, there would always be some competition. And if you are a local service provider, such as a carpenter, roofers, architect, etc., facing a competition means even lesser households to reach. But with a website, you can have a leverage upon that competitor of yours. You can promote yourself effectively with the website and reach out to a wider audience than what you normally serve.
Staying offline limits you to very less kind of promotions. But when you go online, you have a wide horizon. You can reach out to the people through social media, local SEO, forums, and what not. People today prefer searching online if they need any help, rather than looking for pamphlets that were once distributed in their homes.
So going online opens you to a wider array of promotions and methods to reach your target audience.
More trust and higher conversion rate
Sometimes, having a website gives you better credibility than not having one. If your website is built professionally, having all the relevant information as needed by people, they would start trusting you more. And that trust works better in raising the conversion rate on your website.
More people would start buying your services, and your business would bloom even when you are situated locally only.