Can solving lots of mate in one (or two) problems be beneficial?

There is a book titled "Chess: 5334 Problems, Combinations and Games".

From amazon:

"Chess analyzes more than 5,000 unique instructional situations, many taken from real matches, including 306 problems for checkmate in one move, 3,412 mates in two moves, 744 mates in three moves, 600 miniature games, 144 simple endgames, and 128 tournament game combinations."

Mate in one and two problems aren't usually too difficult to solve with experience. But my question is, does the difficulty of the problem matter? Isn't pattern recognition a crucial part of studying chess? I feel like I can get a lot more from simple mate in one (or two) problems then just solving them, and going to the next problem right away.

For example, these simple situations seem to be really beneficial, if I think about them as positions I want to achieve in real games, and if I try to analyze the position.

Or maybe I am dead wrong about this, and I should concentrate on doing problems, that are difficult to solve.

Any opinions?

Yes, it can help you to improve. If the problems are easy to solve it is no drawback. Mate pattern are important, but you should add some more basic tactics.

Looks like the Polgar book - yes think you are right
Personally speaking frequent and focused repetition is the key, to get to know (and crucially be able to recognise in OTB games) the key tactical motifs and common mating patterns.

Tactics decide the majority of club games I play

This Polgar book certainly is good. Especially since the positions come from real games they are realistic and something similar is likely to happen in real games.

Learn one common checkmate pattern at a time and then apply it. ( wiki/Checkmate_pattern )

An end game frequency table lists the most common endings in actual games.
( wiki/Chess_endgame#Frequency_table )

Some might like to first learn the general outlines of chess. ( wiki/Outline_of_chess#Checkmate_patterns )

Then they will practice lots of endgames to be familiar with it. The fun will last longer if a player practices endgames.

It's not by luck that the game finishes the way it does. Some plan from the very start to finish the game with rooks and some plan to capture the opponents rooks from the very start. They probably do that simply to not end the game with rooks. That's why we have a plan in the opening. Can you see your opponents plan? If not, you need to practice endgames to be prepared for their plan.