Single member districts are pretty unrepresentative
You are right to question the value of holding several single-member, First-past-the-post elections. FPTP essentially throws away all votes that are not for the winner. Additionally, it throws away excess votes received by the winner. Throwing away all these votes can result in a set of representatives, which does not reflect the desires of the electorate. The Gerrymanderer exploits this mechanic to achieve their political goals.
In this way, gerrymandering is not a distortion of a well designed system. It is an intentional exacerbation of the problems inherent in a deeply flawed voting system.
Why use districts at all?
There is value in having local representatives who are aware of local concerns, and are accessible to their constituents.
Due to the math of population distribution, at-large elections favor candidates in population centers. This can lead to under-representation of rural voters. Using Using districts helps address this concern.
Districts also reduce voter choices, which can be a positive. California has 53 representatives. Holding one large election to fill all these seats could easily result in 100+ candidates. Expecting voters to research all of these options before heading to the polls places a tremendous burden on them. Limiting voters' choices to just those running in their area simplifies their job.
Is there a better way?
A means of balancing some of these issues is to use fewer, larger, multi-member districts. These ensure better local representation, while reducing the number of wasted votes that results from single-member districts. There are a number of ways to perform a multi-member election. One that is fairly popular is Single-Transferable-Vote.