Why do we need to improve a front three that is one of the best in football and doesn’t need improvement by your definition? Sancho will ruin the chemistry because he will be always play when fit and disrupt the consistent selection of mmm.
I would take MMM over Salah, Firmino and Mane. MMM has better output and are still developing. They can only get better with better coaching. All the players I listed are good enough to provide competition and all of them will cost less than Sancho.The players I mentioned will give us attacking quality as deep as Man City. You just don’t go buy world class players and add them to your team and think things will get better. Some coaching is involved in developing those players which is more important than just buying world class players.
The players you mentioned would not give us quality as deep as City for the simple fact that you think any player on the level of Rashford, Martial, or Greenwood is a threat to their playing time. That's your reason for not wanting Sancho. You purposely do not want players on their level. City on the other hand have Aguero, Jesus, Sterling, Mahrez, Bernardo Silva, and did have Sane, but are selling him and possibly replacing him with Ferran Torres. If you exclude the younger Torress, you could make a case for Aguero, Sterling, Mahrez, and Silva all being of a certain similar quality. Jesus would be more of the quality that you used for the other talents at least in the short term.
I'm going to be upfront, we're not going to be as deep as City even with Sancho. That's 6 players deep for the front 3 spots. You used goals to evaluate MMM compared to Liverpool's (ignoring past seasons).
Aguero - 23 goals, 4 assists
Jesus - 20 goals, 13 assists
Sterling - 27 goals, 8 assists
Mahrez - 12 goals, 16 assists
Silva - 8 goals, 10 assists
vs
Martial - 21 goals, 8 assists
Rashford - 21 goals, 10 assists
Greenwood - 16 goals, 5 assists
James - 4 goals, 7 assists
Replacing James with Traore, or using a youngster like Kubo isn't going to fight back against City's combined front 3. Players like Havertz would be in the same position as Sancho is. Havertz wants to start just as much as Sancho would want to. Would he not be ruining chemistry of Bruno+Pogba or the front 3? Same situation. His price and quality would be similar to Sancho (not in price), but overall factors that lead to the same playing time.
And why would Sancho play every match (55 matches)? He only started about 36 matches this season for Dortmund and it's technically possible to give all 4 players, 36 starts each. That's without taking Bruno's position into account and solely looking at the front 3.
Although I concede to City in terms of depth, I do not want to concede to them quality and potential. If we don't compete by next season, that's fine by me. Having Sancho at the age of 21, Greenwood at the age of 20, Rashford at the age of 24, and Martial aged 25/26 would be a great foundation to outlast City's depth where in Aguero is 33. I also wouldn't bet against Sancho and Greenwood. Sancho putting up those numbers with his technical ability is quite frightening seeing as he's just had his age 19 season, Bundesliga or not. He has the potential to outdo all of City's players, and Greenwood has the ability to outscore all of City's players given time.
Apart from that, I would rather not let any other English club snap up Sancho. You don't want to go up against a talent of his caliber for 10 years. For all this talk of Liverpool's age, Sancho would be the perfect get for them to replace one of them and pair him up with Harvey Elliot (a similar player to 17 yo Sancho and CHO).