I'm not sure what you mean by 'base-load problem', but what I mean is that you need a fossil-fuel base-load.
Of course this is so ambitious that it might never get built but I can definitively tell you that a crane system like this would be barely economical [1] because weights are really expensive but it's a good attempt and can be refined further.
And finally here is an example of a scam concept: [2]
Digging shafts is unaffordable unless you reuse old mine shafts which would reduce the number of shafts in the picture to just a single one. If you can only have one weight per generator that means the system doesn't scale. The power density of lifting a 1000 ton rock 100m high is pathetic. It's just 270kWh. The cost of the concrete is negligible in this scenario but you won't find a generator that is cheap enough to compete with a conventional battery.
However, to stay realistic. Gravity batteries are about as likely to happen as everyone suddenly switching to nuclear power. The odds aren't great.
[0] http://www.eduard-heindl.de/energy-storage/energy-storage-sy...
[1] https://insights.globalspec.com/images/assets/784/10784/Ener...
[2] https://offgridquest.com/images/banners/gravitybattery.png
Basically saying this is wrong.
Technically, base-load refers to the minimum amount of energy demand on a given day. All sources and studies I have are from Germany, but our parliament, their adjacent (technical) offices and the universities here have concluded that "base-load" as a concept is wrong with today's power generation and the way a power grid works. Today they usually talk about residual-load, turning the paradigm around. Regardless of how it works, there are also renewable energies which can fulfil this classical "base-load" idea: Namely organic gas or geothermal power plants.
Why is Germany investing billions in NEW pipeline projects to ship natural gas from Russia for the next few decades? Germany says a lot of nice sweet-nothings, but their actions don't match their words.
Your statement says nothing about the feasibility, just politics.