Do you really need both on-page and off-page for your SEO to work more effectively? The answer is simple, yet complex - It depends.
You will encounter scenarios where clients ask for your help but after auditing or analyzing their website, you find out that they already have a solid on-page SEO foundation and all they need is a robust link-building strategy (a.k.a. off-page SEO). You don't have to force it down their throats that they will still need on-page SEO to begin their campaign with you. Sometimes, you have to listen to the client and match your service offers to their needs.
There will also be situations where you can't do any link-building because of brand constrictions or corporate brand limitations. With that said, all that's left to do is to do on-page SEO. Again, as long as proper expectations are set with the client(s) you're dealing with, meaning they're aware that they're not going to get optimal ranking results from just doing on-page SEO, then you should be good.
At the end of the day, it's all about knowing your client's needs and what they're expecting, plus being able to match what you offer to the said needs and objectives. Not all clients are full-blown SEO clients. Some of them will be one-off, on-page only or purely link-building. You just have to know where they stand and what will work for them.