A Radical Proposal

I've lately been thinking about ability scores – the actual numbers associated with any given ability – and how they might be made to serve a more direct purpose in OD&D and games derivative of it. This has led me down some strange paths, some of which I'll probably start sharing over the coming weeks. For the moment, though, I want to present one of the more radical of them, pertaining to Constitution and the generation of hit points.
My idea, partly inspired by Basic Role-Playing, is that a newly generated character starts the campaign with a number of hit points equal to his Constitution score plus a fixed amount based on his class (the fixed amount is gained at every level, including first). This is obviously a huge change, since it would make 1st-level characters vastly more durable (even with a below average CON score) than standard OD&D characters. Over time, though, the numbers would even out, so that, by 6th or 7th level, the totals would be quite similar on average. To see what I mean, let's compare the average hit points of a Supplement I fighter and magic-user with 11 Constitution to their equivalents under this new system I've imagined. This obviously represents a huge shift in thinking, not simply because of the increased durability of low to mid-level characters, but also because hit point increases are now fixed (+3 per level for formerly d8 hit dice, +2 per level for d6, and +1 per level for d4). This makes a high Constitution an extremely valuable asset, particularly at 1st level. On the other hand, hit points are kept much lower overall. Under Supplement I, a fighter with 18 Constitution and maximum rolls could have almost 100 hit points at 9th level, whereas, under this proposal, a fighter with the same CON would have less than half that. 
Naturally, for the proposal to work, there'd have to be a similar shift in the way that monster hit points were calculated, as well as possibly the damage ranges of weapons. Not having tested this, I don't yet have any way of knowing how this would play out or what sorts of unforeseen consequences might emerge from its adoption. At the moment, it's just an idle thought stemming from my desire to see the numerical scores of abilities in OD&D have more meaning beyond being an index on a chart.