By convention. As hydrogen is the simplest element (in the sense that i has the simplest atom and have the least atomic mass) it becomes a “natural choice” to stay as the conventional zero in electrochemistry.
Since, from physic’s electricity classes we learn that only electric potential differences are measurable, one has always to choose both a situation and an arrangement in order to define a zero potential standard from what someone can measure other potential by difference .
For example, in electrostatics a common choice in theoretical potential considerations is to put the zero potential at the infinity. Even this is not concretely attainable, it’s fine to a theoretical exercise.
But in electrochemistry the things are pretty more concrete (in fact, are concrete). You choose hydrogen, in its “more natural form” (gas) at atmosferic pressure and under tge temperature of 25°C = 77°F. Under this conditions, the conventional standard potential is zero
There are different approaching points here. One is history: The hydrogen electrode has been used forever and people are used to defining values relative to it, so why not continue?
A second point of approach is the following: You cannot measure absolute potentials; you needsome kind of a reference. The choice was completely arbitrary. However, there are some ‘rationalisations’ (that probably only turned up after hydrogen was already used):
Hydrogen is the first element in the periodic system. It is nice to have ‘number one’ as your reference.
The potential of hydrogen (hydrogen gas at 1 bar in an acidic solution of pH 0) is approximately equivalent to that encountered in 1 molar acidic solutions (sulphuric, hydrochloric, nitric acid etc.). Probably even predating the selection of hydrogen, metals that dissolved in 1 molar acid were termed non-noble and those that resisted the acid were noble. Using the hydrogen potential as a zero-point, the non-noble metals have a negative standard potential while noble ones have a positive. An easy way to distinguish noble metals just by a number.
But just to restate: The choice of the electrode as a standard was likely before the second implication was fully realised.