Is it wrong to write a coefficient of 1 in a chemical equation?
It is not wrong, per se, but it goes against conventions.
These rules are in place to simplify how we write formulas and equations, etc.
If we did write the $1$ all the time, then perhaps we would write it for a chemical formula, and water would be $\ce{H2O1}$, for instance.
If you want to write it as a reminder and placeholder that is totally fine.
A teacher might say that they have a rule, or that they want you to follow standard convention. You should do this if requested. When I taught, I would offer to students that it is OK if they want to do it to get in good habit of always writing coefficient.
All that being said, IUPAC guidelines say to write the species with no coefficient if the coefficient is one. So, technically it is not to the standard, but does not make it less clear, so use it in your work, but if you are submitting as classwork follow the protocol of the class.
Below is cited a brief note to this from the The ACS Style Guide[1].

➤ Specify the number of each species (molecules, atoms, ions, etc.) of reactants and products by a numeral written on the line and closed up to the symbol.
$$\ce{2Al + 6NaOH -&gt; 2Na3AlO3 + 3H2 }$$
➤ To indicate the aqueous, solid, liquid, or gas state, use the appropriate abbreviations on the line, in parentheses, and with no space preceding them.
$$\ce{Ag(s) + H+(aq) + Cl–(aq) -&gt; AgCl(s) + ½H2(g)}\\
  \ce{4FeS(s) + 7O2(g) -&gt; 2Fe2O3(s) + 4SO2(g)}$$

Within these few lines, it is stated to write a numeral, but then it is omitted when it is $1$.
House rules prevail, as this is commonly accepted practice.
Reference:
[1]: The ACS Style Guide: Effective Communication of Scientific Information; Coghill, A. M., Garson, L. R., Eds.; Oxford University Press: New York, NY, 2006(pdf).