I think it's pointless to talk in general terms like "using the big ring only" or "using the small ring sometimes." Is your big ring 53 teeth, 52, or maybe only 48? What's the range of your cassette? 11-27, 12-34, or ?
I could be on my small ring and the middle of my cassette with a higher ratio than someone on his big ring and biggest cog.
I used to ride with a friend who would sometimes set a goal for himself to not leave his big ring through an entire ride. He was a strong climber and had personal ambitions to improve his mashing ability. He might just as well have chosen to stay on cogs 21 teeth or smaller regardless of chainring selection, but it's easier to watch and it's also psychologically more impactful when you just decide to not shift down in the front.
In any case, it's really about your current fitness level vs. your goals. Some guys might want to never let their cadence drop below 90, or power never less than 150W (these can be impractical on mixed terrain; more feasible on flats). Personally, I like developing my overall riding skills. I want to improve my abilities to spin fast, to mash hard, to keep a moderate effort for increasing durations, etc. Mostly, I want to get better/faster at riding in real world scenarios, where a variety of skills are necessary. Sometimes others give me worthwhile advice, but I would disregard anything as general as "don't use your big ring."