Yes this is a good question.
Personally, I don't place any importance on this at all UNLESS you are using the Greek system of whole sign houses, and even then I'm not sure what weight I'd give it.
Even if you use the Western whole sign system of houses, at least part of the sign following the one on the cusp, is within the House. Once you move on to Equal space or Equal time systems of Houses, then it's quite possible to get intercepted signs, two houses with the same sign on the cusp, etc. The link between signs and houses in the sense implied in the question is broken.
What matters is where the planets are both by house and sign.
The modern psychological view attempts to simplify as much as possible, hence the so called ABC system which believes that Mars = Aries = First House (and so on). The abler psychological Astrologers actually do warn against taking this view too seriously. It's better to use the traditional term 'co-significator' which implicitly shows that the sign and house are not the same thing.
Now, Mars is better placed in Scorpio, where it has more dignity (and Saturn in Aquarius). And its favourite House placement (it's Joy) is the sixth and if you look at the Joys of the other planets, they don't correspond with the Sign/House number.
In other words a lot of nuance and meaning is lost if you go down the ABC path and whilst it may make Astrology easier for the beginner, the chances are that even when they become acomplished, those who started with that system will keep to it and miss out on the wider stuff. It leads to blinkered vision.
