I would say the opposite: there's ALREADY many BTC in circulation, AND we seem to have hit a wall into the mainstream that takes a bit of time to go down.
So the question is: will people want to pay more for one BTC?
My answer is no. If they would, they did already.

Halving of the reward doesn't say anything to the upcoming mainstream user, and they will only pay what they think it's worth it.

My forecast is that when the halve will come, miners will raise the price to stay afloat.
BUT then people won't pay that much more.
Now, the only problem here is if miners are already earning much more than a Bitcoin is worth.
If they do, then no problem.
If they don't, then some inevitably will close the shop.

And then, we will have a drop in value instead than an increase, because when the community will see that people are NOT eager to pay much more than the actual price, there will be a fall of reputation.
Many mining companies will close because of this and there will be a mini-collapse of Bitcoin this year because of this.

THEN in the future the value will rise again, but I wouldn't expect it anytime this year.

This will allow for a REDISTRIBUTION of Bitcoin nodes. Part of Bitcoin philosophy.

I HOPE I am wrong, but this is my feeling at the moment.