The easiest way to get to the desktop version of a website is by selecting the desktop view link on the page itself - if it is provieded! Not every website has this option, so of course your described methods are usefull in this cases as a quick workaround.
On Mozilla Firefox, you can also do this by opening the menu to the right(three dots on top of each other) and checking "request desktop site". Requesting desktop is particularly useful for youtube videos of songs, because this way, you can lock your mobile device and still listen to the song, which is not possible through the youtube app.
If you have installed the mobile version of Chrome on your device with Android or iOS, you can enter the web in question and ask to see the desktop version from the browser menu. To do so, on either device, open Google Chrome and the page you want to visit. Once there press on the menu (on iOS there are three horizontal lines on top of each other and on Android they are three points, both are on the right corner) and look for the option "See as on a computer" that you can mark to that stays permanently and applies to each website you visit