There is - it just doesn't use metal springs
Metal springs have numerous failure modes. In tension, they only remain "springs" for a certain point, after which they simply become wires/rods (which also have a Young's modulus, but in a different way). In compression, they also only remain "springs" until the coils touch, at which point again you have a solid rod. Coiled springs of any type simply don't work well for this.
What does work well is any compressible liquid or gas. As anyone who's bounced a ball knows, compressible gases are a near-perfect spring (and by extension liquids too; they just generally need more force to compress). Gases and liquids can also be compressed over an extremely wide range of pressures, only limited by the pressure/volume at which a phase change (gas<->liquid or liquid<->solid) starts to take place. An "accumulator" pressure vessel is pumped up to pressure for energy storage, and energy release is simply handled by letting the gas/liquid flow out through a turbine.
This is one type of system that has been used for kinetic energy recovery systems in cars. As per Wikipedia on KERS, Bosch and PSA developed a hydraulic KERS system for road cars in 2015. Some places are still looking into the concept.
The problem is that this design has competition from other methods of energy storage which are generally preferable. A pressure-storage system inherently needs two tanks, one for the liquid under pressure and one for the liquid not under pressure, so for starters you've made it larger. And a high-pressure storage tank requires significant effort in construction otherwise you've essentially created a very powerful fragmentation bomb (which of course has been why hydrogen-powered vehicles took so long to come around).
For mechanical energy storage, flywheels generally give higher energy density for smaller applications like cars; and on a larger scale, gravity storage (pumped-hydro) schemes give you scaleability with relatively low cost. Pressure storage can't generally compete with either (although you could think of pumped-hydro as a very large pressure-storage system running at very low pressures).
And that's just mechanical. Electrical storage is also popular, of course. For small applications, KERS systems today generally use supercapacitors because they give very high energy density with the added bonus of being able to control the energy output very accurately; and longer-term electrical storage of course uses batteries for the same reason. There are currently not many options for larger-scale electrical storage, but flow batteries have been discussed conceptually for a while, and the technology is starting to come around. This is especially relevant in the context of renewable energy sources, of course, where there is a definite need to store energy whilst the renewable source is not generating.
TLDR: Yes, you can do it, and people have tried it. And people haven't then taken it further, for reasons.