Good question!
It is generally good to avoid checks. While the following moves after a check may not affect the player on a small scale; checks generally help the attacking player. Even if the ensuing moves won't cause problems for the attacked player, checks are avoided by principal due to the following reasons:
The check helps enemy development
The attacking piece is devolved while attacking the enemy king, this forces the enemy player to lose tempo and momentum. Due to the fact that the enemy player must block the check or move out of check.
This concept is extremely important in the opening, as the goal is to get your pieces out as fast as possible. If the flow of development is interrupted by a check, the attacking player will be two moves up on the enemy player
Checks win momentum and tempo
One of the critical parts of chess is having the momentum. When an enemy king is checked it starts to develop a momentum and build a tempo of attack
The concept of momentum is simple, if you are replying to an attack, then you don't have the momentum, the enemy does.
However, if you attack, and your opponent has to reply, than you have the momentum, and are one move up on your opponent
Side affects
Pieces blocking check are pinned and can be pressured later in the game, also if the checked king ever has to move out of check before castling it will no longer be able to castle putting the attacked king at a major disadvantage
Saving time
In blitz and bullet, the key reason for avoiding checks is the amount of time it takes to analyze whether or not a check will lead to a major attack takes to much time. So the check is blocked
Better safe than sorry!
I hope this helps!