Let me give you another example. I'm a biker. When I'm travelling sometimes I see a scene worth a photo. I could use my phone, but that doesn't allow the control of the image that I want. I have a full-frame kit. To take that on the bike it needs to go in a bag somewhere, strapped to the bike. This makes the process of stopping for a photo somewhat cumbersome and reduces the fin of the trip. So I have another kit. It's a Panasonic GX80 along with the 12-32 and 35-100 zooms. That whole kit fits into a little belt bag. Now I just have to stop, take out the camera, change the lens if necessary, and take my shots. Put it all back again and carry on. Now, being mainly an FF users I'm accustomed to the settings that I want for FF to achieve the shot I want to take. Equivalence tells me what settings to use on the GX80. I've used it enough now that I don't have to think about it. But it is the equivalence theory that explains what is the basis of those decisions. You see many mFT and APS-C users just using the settings for FF, because that is what they see in discussion. No idea that 'f/8 and be there' is 'f/5.6 and be there' in APS-C and 'f/4 and be there' in mFT. The point really is knowing what settings to use if you move from system to system - or if you're a Canon or Nikon user, how to change settings if you're using the 'interchangeable body' idea. One set of lenses, bodies of different sensor size to optimise for different shooting situations. No one'e ever going to do equivalence calculations on the fly - but it gives the underpinning for how to handle the different sensor sizes situation.
Old fogeys like us were brought up mostly in a single format world, where one 'sensor size' had dominance, mostly caused by what processing labs were willing to do - and the constraints if you used a format which needed specialist processing. With digital it really doesn't matter much what the sensor size is. ILC's have some constraints. Equivalence also comes in handy making purchasing decisions, letting you understand what you might get from different options with different sensor sizes. For instance, I see a lot of people shelling out for FF when for the photography they do a smaller format would cover everything they do with the same quality, but they paid the cost of not understanding equivalence in terms of price, size and weight.