Yes, you can use a normal set-top box for viewing television channels on modern TVs but the viewer experience will differ from a case to case basis. Let me explain it to you taking the Tata Sky connection as an example.
Tata Sky has 4 different types of set-top boxes such as Tata Sky SD, HD, +HD, and 4K. A normal set-top box will generally be an SD one and is well-enough to view SD channels in normal size TV. However, if you own a TV with a bigger screen such as 32 inches or 42inch or 55 inches than you may not get a better output in SD channels. So, it will be necessary for you to upgrade to HD channels and also get an HD compatible set-top box.
Moreover, for getting good quality video output in 16:9 aspect ratio you will need an HD set-top box. Other important features when you upgrade your set-top box is that most service providers offer the feature to download or schedule TV programs so that you can watch it at your own convenience and not necessary when it is actually broadcasted. This is helpful for working personnel and students who have a fixed schedule of work or classes.
Overall, you can keep using your normal set-top box while viewing cable channels on your standard TV but for an enhanced experience and if you are considering to purchase a bigger TV, an upgrade to the set-top box is also very essential otherwise you won't get better viewing satisfaction.
