Instant deaths are always cheap in games, but there are games that find ways to make up for the cheapness. In 2D, for example, the Castlevania games always have checkpoints, or Mario games just have short stages in general. Doing things like these in a 2D game removes that "cheap" feeling.
In 3D games, like said already, the Sands Trilogy in Prince of Persia added the rewind feature, so unless you kept repeating the mistake, or were unfortunate enough to be caught in a platforming segment without any sand, you weren't given an instant death. Or, for example, Uncharted. When an instant death occurs (maybe falling into a hole, or hit with a trap), there are checkpoints that take you back only a small amount of distance.
When these instant deaths are things that force you to return to the title screen or from your last save, they can be a heavy annoyance. There ARE ways to make games harder without frustrating the player. Checkpoints and autosaves do NOT make the game worse, but are actually far more convenient for the player. Instead of a death forcing you to repeat a segment, and probably several prior segments due to saving, instead, make the segments harder.
One thing I appreciated about the earlier Castlevania games and especially the Souls titles is the way they handle their difficulty, and I think the next Castlevania should apply this. They don't swarm you with enemies, and they don't give them an unnecessary amount of health (coughLoS2cough). Instead, they give you a ton of unique enemies with different patterns, with enough intelligence to fight you without making the game overly difficult.
Games like Prince of Persia have some pretty shitty higher difficulty levels. All that changes is that you take more damage, and enemies have more health. This is NOT a fun way of making the game harder, it just makes the battle more tedious. The Metroidvanias with selectable difficulties had this problem as well. Instead of ramping up the amount of damage you take and heavily dialing down the amount of damage you dish out, only changes those a bit, while adding new moves to the bosses or enemies, change their patterns, make them faster or stronger, or hell, even add new enemies.
tl;dr: If you're gonna have instant deaths, find a way to make them feel less cheap. And if you're gonna make the game hard, don't make it artificially difficult.