Training with a good mix of hard and easy sessions will absolutely make you fitter. However, key to this is allowing the body to recover properly between each session. (Call it Balance)
Each time you stress your body - running faster, riding longer, building strength, you set it up for physiological adaptations. When you stop, refuel well and recover, that is when that adaptation happens. Think of it like building a house. You build a foundation, get it settled and then build the next layer.
(Another way of thinking about it : You dig a hole, and that’s OK. “But you have to fill the hole and then make a hill to improve your performance. The worst thing you can do is dig a hole and keep on digging. If you don’t rest properly, you can sabotage your training.”)
Recovery includes those short rests in between interval sessions (like run 100m fast and then rest or walk for 20seconds) and also importantly the days you just take it easy.
Lots of good sleep, a movie on the couch, an easy walk with the family - all accompanied by some good fuel (a normal healthy does of fruit and veges along with a great source of protein suffices for most of us), plenty of water...and recovery sorted.
So in short - you can train too much (and yes you can recover too much too - that is called detraining), but getting the balance right for your lifestyle and stage of fitness is super important.