One of those "1 Farad" car stereo caps (not the classiest example) can store 72 joules (watt-seconds). So to handle a 1kW excursion for 5 seconds, would take over 70 of them. Possible, yes. But probably not worthwhile.
The frustrating thing about this article is that it keeps conflating fundamental physical problems (like needing to store energy to deal with peaks), with the limitations of currently-productized circuit topologies. It's not hard to imagine an inverter that would do something similar to MPPT without needing to pull/dump the maximum power possible, would manage a small bit of local storage (a combination of caps and abused batteries), and could intelligently load shed (with "kind" brownouts) on multiple outlets.
It's also not hard to imagine an inverter (brushless motor) air conditioner that would be a lot kinder of a load, and could even operate at variable power.
But of course with the current state of homebuilding, these are bespoke ideas better filed as "off the grid". Which is the entire larger point - an "off the grid" system fundamentally costs more in materials and also presently application engineering time, than the on-grid systems being sold to homeowners.
(Although I do have to wonder about adding a piece to the current puzzle that would generate/manage a local grid frequency, and shed excess power using off-the-shelf electric heaters.)