Last time I switched, I had to compare unit price. I don’t have gas, and my electricity is day/night tariff. After comparing. Bulb happened to have all three (day cost, night cost and standing charge) cheaper than my ongoing tariff with British Gas. Here’s how it looked in my spreadsheet:
I agree with you, monthly price is nothing without context. BUT, what is easily comparable is unit cost. If Monzo would ask us to retype cost from our most recent bill (3 values, seems low effort), take our postcode and then compare it to deals across suppliers, this is what would be my preferred solution. Monzo could store our cost per unit, and notify us if they find something that seems better at a later date.
If all prices per unit are cheaper, then it’s no brainer - as long as you don’t get yourself stuck in lousy deal for 2 years ahead, most likely you should switch. I’m speculating that for many users who didn’t change their tariff recently, a comparison should end with a full set of unit prices being very clearly cheaper than their current tariff. It’s difficult to tell how many users could fall under this simplest scenario, but knowing how many people don’t switch at all… it could be a good chunk of users! 
But there are problems that escape simple ‘compare unit price and pick one that’s cheapest’. It might be that price per unit is cheaper for day, but more expensive for night, or standing charge differs etc… then it would require further data input from user to really make a spreadsheet to calculate sums in full (based on last 3 months usage?). That’s a bit more hassle to make it work. I’m not sure if Monzo wouldn’t be entering ‘uswitch’ comaprison area a bit too much, but I totally wouldn’t mind if they do this better. I’m not a fan of comparison sites, they earn commission just like Monzo is, but I’d trust Monzo over ‘uswitch’ and others.
Valerio mentioned that they don’t get any cut from Savings section yet. It kinda shows how important this aspect is. I quoted his reply below: