There's nothing ethically/morally wrong with using a template as long as you abide by its licensing. That's the big thing to keep in mind when using premade website templates: make sure you understand the terms of its license, and make sure you use of it falls within the rights of the license.

Many website templates are open source or distributed under the Creative Commons, and in those cases, you're generally OK to use them and change them however you need. Sometimes the license will require you to include attribution in the final product, but I would recommend you do even if it's not required. Since you didn't create the template, including a link in the footer back to the original author is just a nice way of saying "thank you" and encouraging the designer to keep making free templates. Paid templates are usually pretty similar, with the exception that you probably can't access the source templates/assets without paying for it. And when you do, just keep in mind the terms of the license, as it probably is licensed per-site, so you can't reuse the same template across multiple projects.

As for whether you should use templates, it is entirely up to where you want to take your career path. If you want to get in the freelancing business, making websites for clients, then it's probably best to learn these design skills yourself and make your own templates, to make yourself stand out from amongst the crowd. If you're building sites for yourself (your landing page/blog, project docuemntation websites, company's internal sites, etc.), go ahead and use a template!