Generally for simple trips ABA, ABCBA type journeys with no open jaws then it will be cheaper to fly on one airline than a of mix carriers, and especially for ABA trips. This is is because two competing carriers fares will not generally combine, and thus either only a fully interline or IATA fare can be used to price the itinerary. IATA fares are industry fares set high and accepted by all carriers.
For more complex trips including connections then it is not so clear cut. Airlines working together under anti trust and revenue or profit share agreements may follow the principle of metal neutral selling, and therefore the price will be the same whether it is the same carrier throughout the whole trip or a change of carrier. However, the availability of the seats may still give rise spot price differences either by routing or carrier.
Outside of alliances then you are into the world of bilateral interline agreements and the special prorate agreements agreed between the carriers. More or less attractive agreements will be reflected in the validating ticketing carriers own pricing.
The pricing of multi city trips is not going to be any easier, especially if you are travelling into obscure places where the carriers do not have interline e ticketing agreements with each other. For example, the big European flag carriers the many domestic airlines in china. This would mean not only would multiple carriers fares need to be used to price the trip but the itinerary would need to be ticketed on multiple carriers ticket stock.
It seems likely to me that comparison sites do not handle these complex cases very well ( lean thinking around runners, repeaters and strangers may suggest why bother with the complexity)
Sorry if all of that didn’t make any sense 😆