For a genuinely quick car yes it's much cheaper. No denying that.
My Fiesta with n/a zetec and a short gearbox felt fast enough with 814kg including me as driver and a full tank of fuel and the interior. That was 195bhp and 150lbft. With the Clio the same figures won't feel very quick, it's got another 300kg on top. Boost required!
I tend to think of roughly (include weight of driver / passenger):
150bhp per tonne = ok for getting started on trackdays, but you'll get stuck behind people a lot and frustrated if your car handles well so you catch them in the bends but then cant get past them on the straights and arent allowed to overtake them on the bends
(e.g Standard 172)
At this level on medium speed bends after a short straight you may find your car is so slow you cant enjoy the corner as the car cant accelerate to the speed you need to in order for it to feel like a corner
175bhp per tonne = At least you can pass most normal cars just about on a long straight, but still pretty hard work
(e.g throttle bodies 172 or RS2 and a set of 197 cams, hot cams on standard inlet just about)
At this level on high speed bends after a short straight you may find your car is so slow you cant enjoy the corner as the car cant accelerate to the speed you need to in order for it to feel like a corner
200bhp per tonne = Will pass most normal cars relatively easy on the straights so little chance of ending up too stuck behind someone too often
(e.g as above but stripped right out, or bodies plus cams, or low pressure turbo)
At this level on very high speed bends after a short straight you may find your car is so slow you cant enjoy the corner as the car cant accelerate to the speed you need to in order for it to feel like a corner
250bhp per tonne = Starting to actually be a fast car, should be able to get past M3's and the like
(e.g low pressure turbo and stripped, or mega lightweight cars with bodies and cams like the burspeed, or a high pressure turbo)
At this level I cant think of any bends on uk tracks you wont have enough power to really exploit your cars handling by getting upto the max speed it can go through them at.
More than that = TBH the extra pace now only really helps in the middle of long straights as you cant really use it coming out of corners very well anymore and as per above its not really needed to get you upto speed on the way into bends either.
Ideal if you want to race people down dual carriageways etc, but in a FWD hatch on track its not really any advantage over the 250bhp or so mark really.
If you do want to go for something like 300bhp per tonne, I would do it by having 300bhp and stripping the car, rather than having 400bhp and having to have huge brakes etc