Australia

So, we have a "tiny roof project" on our rooftop. And it really is tiny since we have a two bedroom home

For 9 hours a day (in winter - 11 hours in summer) they produce four times more power than our peak consumption. When it's cloudy... it produces about twice our peak consumption. In hindsight, we probably could have saved money with an even smaller system... but a bit of headroom is nice and it wouldn't have saved much money, since wiring and the inverter were about the same (we installed the maximum number of panels our inverter can handle).

We also have power now even if the grid goes down during the day - doesn't happen often but it does happen occasionally.

It reduces our electricity bill by between $3 and $9 per day depending on the season.

If we're at home and use a lot of power, we sell between $1.50 and $2 to the grid. If we're out of town and use no power during the day (except the fridge, etc) we sell about $3 per day to the grid.

At that rate, it will only take two years to pay off the upfront installation cost... the inverter has a 10 year warranty and the solar panels have a 30 year warranty. So I'm fairly confident it will last longer than two years.

If we couldn't sell power to the grid, it'd still pay for itself in less than 3 years. Over the life of the system it should easily pay for itself ten times over.

Is it "more economical to put them in fields"? I haven't had quotes for that, we didn't consider it as there are no fields nearby. But our panels are screwed into the roof which took a couple hours. If we put them in fields they would've had to dig concrete footings, put posts in the ground, etc which likely would've been a much bigger project involving multiple contractors instead of just an electrician and two apprentices. There would also need to be underground or overhead wiring to our which, if you do it safely, is a major headache in it's own right.

I'm pretty sure you're wrong about placing them in the field being cheaper. You're underestimating cost and complexity of getting the power from the panels to your home.

The fact is rooftop solar is very simple and very cheap.

As for the "asphalt shingle and roof" being too weak... we have four aluminium bars almost the full length of the building screwed down on the outside of the roof, and the panels are screwed to that. The bars alone are more than strong enough and they spread the load evenly over the whole roof structure - there would be minimal load on the roof and I'm sure it'd work fine on shingles.