There is zero chance right now of any battery storage being in the $3/kwh range. Even in the manager-of-the-battery-factory-took-some-home-for-cost situation.
A Tesla battery is roughly 80kWh, and costs $5k - $10k. If it were $3/kWh then it would cost $240. And since most home batteries are 10kWh they would cost $30 (plus electrician labor costs and wiring).
Solar panels have indeed become much cheaper, although it is important to distinguish between energy "provided" and energy "stored." Which why the combination is so important. It is often great to look at solar in terms of a "solar day" which is defined as the hours during which the panels deliver peak capacity. On my house, there is about 6kW of solar panels, and under optimum productions they produce for 5 hours in a day, so a total of 30kWh. What gets to the house or the grid is reduced by efficiency losses and the difference between performance under "standard test conditions"[1] and what is actually their environment. My house reliably produces just over 5kW at its peak or about 25kWh in a solar day.
In California, if you are tied to the grid as my system is, you are still at the mercy for how much the power company will credit you for power you generate vs charge you for power you consume. That has been a source of argument hear for the last 20 years. With sufficient local storage, you can completely disconnect from the grid and that removes this pricing power of the power company over your energy production. Something I hope to do within the next 5 years.
[1] This is sort of the MPG equivalent rating for solar panels, good for comparing panels to other panels but bad for guessing how much power they will produce for you.
I've been considering it, and I figured $2 CAD/kW is the 10-year break even point for me, which would be amazing since you can get a 10 year interest free loan for it.
I googled around for a while, and found pioneersolarenergy.com. Super helpful, good shipping price, etc.
As well as the 10 year interest free loan check if your province has any rebates. The "Greener Homes" grant gave me $5k (So I only have $8k on the loan). It just made 1000 kWh in June, I'm super happy.
And I'm not sure how you were trying to relate that to battery storage.