Memorization vs Skill
Only at the grandmaster level is memorizing hundreds of lines necessary. At the amateur level just pick out a favorite opening for White and Black and stick with it.
As White I always played the English opening in all my tournaments and got to USCF 1450 before I quit playing tournaments. Playing Black I would almost always use the Caro Kann or Lasker Defense. I didn't try to learn a half dozen openings. I never started playing chess until I was an adult though.

You only need to know one line against each of those cheap traps, though.
For instance, the Englund Gambit (played by Black, after 1. d4 e5) is worthless if White answers it properly. After 1. d4 e5 2. dxe4 Nc6 3. Nf3 Qe7 4. Nc3! White already has a big advantage, and Black isn't getting the trap he intended.

You need to memorize a lot of branches to get past move four. Understanding aids memory.
You need to rethink your comparison to plagiarism.

Im beginning to notice a trend. People who like to complain about theory usually have an elo of under 1000. Also the comparison is absolutely terrible for multiple reasons.
1. If somone has already invented a bicycle (which can be compared to an opening) why would you try your hardest to reinvent the bike when it has already been invented for you. What this means is why should you try to create your own theory from scratch when the best has already been made, and you are just wasting your time.
2. The point of theory isn't to spit out moves, but to understand the concepts of the moves and what they are trying to accomplish, so instead of plagarizing, its just seeing the main ideas of someones work and using it in your own, except instead of simply plagarizing, you are citing your sources. What I mean by that is its not plagarism because you aren't making your own openings and claiming to have been the first to play them. You are playing an opening called "The Ruy Lopez" because he made it popular.
3. You aren't plagarizing because your getting all of the moves wrong anyway.

This kind of attitude will hold you back, not just in chess but in anything.
Making things harder on yourself then wearing it like a badge of honor isn't practical or admirable. Use the tools you have available to do the best job you can. That will always mean modern tools and techniques give you more than past masters had.
Also your comparison to Fischer is out of place since he memorized an enormous amount. There are multiple stories of other GMs marveling at his knowledge.
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As for players who do the same thing over and over... you have to start somewhere. If they play, for example, a London setup and try to attack the kingside the same way in every game, sure that's low tier compared to a master, but it's better than nothing. As they continue to learn and get more experience they'll branch out to new ideas and patterns.
... but this is something I see more often at, let's say, the 1700 level (using the same few ideas)... you're not even 1000.

Oh oops, thanks for pointing it out. I stopped reading the latest comment after the first line when i realized it was totally wrong.

You should read some posts by players who know what they are talking about. Your perception of players spitting out moves they don’t understand simply from memory is incredibly naive.
After four moves have been played, there are 18 billion possible positions. To remember anything that far, you must also understand why 17.99 billion of those positions are completely and totally lost for one side. That still leaves a million to memorize. No one has done so.

You should read some posts by players who know what they are talking about. Your perception of players spitting out moves they don’t understand simply from memory is incredibly naive.
After four moves have been played, there are 18 billion possible positions. To remember anything that far, you must also understand why 17.99 billion of those positions are completely and totally lost for one side. That still leaves a million to memorize. No one has done so.
Like unicorn pointed out, that person probably knows what they're saying is completely wrong so

You should read some posts by players who know what they are talking about. Your perception of players spitting out moves they don’t understand simply from memory is incredibly naive.
After four moves have been played, there are 18 billion possible positions. To remember anything that far, you must also understand why 17.99 billion of those positions are completely and totally lost for one side. That still leaves a million to memorize. No one has done so.
Like unicorn pointed out, that person probably knows what they're saying is completely wrong so
The idea that one must be wholly original in everything holds many people back not only in chess, but in every human endeavor where skill development is useful.