There's nothing inherently wrong with a lives system, and nothing inherently right with it. The arcade games which popularized the idea (and inspired other games which also popularized it) needed a solid way to prevent people from progressing and keep dropping quarters; lives worked for them.
For other style of game, however, I can't say I'm fond of the idea. I don't mind being punished for dying, and the tension of being low on resources and needing to navigate a dangerous area with tonnes of lost progress on your mind is good fun (Hollow Knight did this well). However, the Umihara Kawase games illustrate exactly why lives systems can become unnecessarily frustrating.
The first two games are hard as nails, but mostly due to poor controls and Umihara's sluggish movement/jumping. Every enemy is instant death, and if any enemies don't kill you on contact, then they'll surely knock you into a pit. They also spawn randomly and respawn infinitely, which is awful game design. This kind of all-or-nothing gameplay doesn't mesh with the core gameplay, which is a puzzle platformer. I played each game for several hours before becoming too fed up to go on.
>welp, looks like i died on this puzzle whose solution i realized half an hour ago but which i haven't completed because the bungee physics didn't co-operate
>welp, looks like i died on this "boss" whose strategy apparently involves hanging on the underside of a platform for five minutes and ignoring him
>gotta redo the half-dozen levels to get here for the umpteenth time, since i clearly had problems with them, right?
It turned a charming little game into a merciless grind. The third game did away with the lives system, and simply had the player unlock levels. Bonus lives were replaced with collectibles which unlocked key art, additional characters, and so on. It's certainly a less punishing game, but I had a MUCH better time playing it since it didn't force me to redo pedantic sections in between the crushingly difficult parts. The controls and level design were better, too, but that's icing on the cake.