After reading comments under 
But the core question still stands:
What makes Steem valuable? What gives us a reason to think that Steem (and Steem Power) will appreciate in value despite the inherent inflation?
In my view the answer is very simple: it's the Steem Dollar.
The existence of Steem Dollar (SD) is the main reason here. And it's a very solid reason.
Now I'll try to explain why. But first, let's deal with some misconceptions.
I could understand that if Steem price was supported by companies or ads therefore creating revenue in the form of Steem, sustaining creators and payouts. But as far as I know there's no plans for that in the near future.
A similar issue is raised by 
I think the problem with many of us who are investors is a lack of direction in regards to monetization from the Owners. What you just mentioned sounds interesting but I have never seen an article or monetization plan from Ned and Dan. I would love to invest more but I can't just invest on a hope and a dream, we need to see the future vision to earn money. All we are seeing is how to give it away and dilute our investments thus far.
So it's a question about plans for monetization of the Steem ecosystem. FB and other social networks have big market value because they have the potential to make money through advertising - by selling their users' data. Does Steem have a similar potential and will it follow this path? Some people expect this to happen, e.g. 
Not sure why you think companies won't purchase Steem for sponsorship or ads in the future. The ad model will be different than traditional online advertising, but imagine any company can buy $1 million worth of Steem, probably be able to payout a few hundred a day a day or $100k/yr in rewards as blogger sponsorship or to promote their own posts. That's valuable. We're also not even including the payments/commerce part of the ecosystem. That's valuable too as well as the network effect.
Here is the thing: Steem could do that but I think it won't be necessary. There is a much bigger fish to fry: creating a ubiquitous monetary system, with Steem Dollar as its main currency.
Demand for SD will drive demand for Steem (and Steem Power). Why? Because SD is backed by Steem, it's an IOU guaranteed by the Steem blockchain. SD is just plain Steem under the hood.
Steem Dollar? Why would I want it?
This part is easy: if Steem as a social network becomes huge and, as a result, SD becomes a ubiquitous currency, people will want to acquire SD for daily shopping. More and more people (even those not interested in the social network aspect) will either earn or acquire SD and keep it in their wallets - not only as an investment (it pays a nice interest rate) but also because they could buy and sell stuff for SD on a daily basis. So there will be a tremendous amount of SD just sitting in people's wallets - ready to be spent when buying stuff, or just received from selling stuff.
If you think carefully, this is exactly the same vision as Bitcoin supporters have. Why does Bitcoin have value? Because there are people who expect it to become a ubiquitous currency sitting in the wallets of millions of people - the same argumentation applies both for Bitcoin and Steem Dollar.
Some people have a different explanation: for them Bitcoin has value because they believe that eventually a sustainable business model will emerge which will be based on the revenue generated from transaction fees. Again, this a huge misconception. If you do the math, you'll see that transaction fees would have to rise significantly (which would kill Bitcoin as a payment system) to be able to sustain Bitcoin economy in the long run.
Anyway, after 8 years of its existence, most people understand the potential of Bitcoin investment.
You buy Bitcoin because you think it will appreciate in the future, as with most other investments.
So why the same logic cannot be applied to Steem? There seems to be another misconception which prevents this. This is what
The difference is that if you buy Bitcoin you buy into the blockchain tech, your money is "safe" and should appreciate as long as Bitcoin works as it's scarce. That's why it has been appreciating annually since it was created.
And the above view is backed by this argumentation:
Steem on the contrary is a highly inflationary currency, you buy on a Monday and by Friday there's thousands more Steems created, so the price will go down. What value does it have for the buyer? I get that there's value in content, but there's a disconnection there. Buying Steem doesn't give anything back to the investor, it'll always dilute unless it's supported monthly by an external agent like a company or via ads/revenue. Speculators and traders won't cut it.
And here is the crux of the matter. Bitcoin is perceived as a deflationary currency, while Steem is treated (rightly so) as "highly inflationary currency". It's a false perception (in reality Bitcoin is also highly inflationary) but still, perception is all that matters. Steem takes an undeserved beating here. It's undeserved but it's hard to fight with perceptions so I think we must identify and address the underlying problem.
Why is Bitcoin perceived as deflationary?
Most probably because it has a well defined limit to its supply. There will never be more than 21M Bitcoins in existence. Nobody reading this will be alive when this limit kicks in (year 2140) and no investment horizon extends that long, but still it makes a significant psychological impact: yeah, there is some inflation but it is decreasing in a predictable manner and eventually it will stop.
People believe it matters, and, as a result, it does matter.
Conclusion
Maybe we should consider, purely for psychological reasons, establishing a cap for Steem supply in the very long run and decrease Steem inflation a bit every couple of years. This will not affect in any significant way our economic model for the next 100 years but it may create a positive signal in the eyes of investors.
Maybe
It's like you are trying to sell me US dollars "to keep the economy up".
The FED can afford to get away with an infinite inflation because US dollar is still perceived as the ultimate currency. Steem is not in this position (yet) so maybe we should acquire a more humble approach. At this stage, our benchmark is Bitcoin, not fiat money. Once we have a total supply limit hard-coded in the blockchain, nobody could really argue with this claim:
If Bitcoin economically makes sense, so does Steem.
EDIT: Initially I thought my argumentation would end here, but now I think there is an extra twist to it.
Is inflation such a bad thing?
The answer is no! Actually, inflation is crucial when you try to bootstrap a new currency, as it enables its distribution to a wider population. You just cannot do it without inflation. Bitcoin would have never taken off if all tokens had been already created and stayed in the hands of the first initial miners.
Without inflation Steem would fail because the whole ecosystem wouldn't be able to expand. So inflation is an asset, not a liability, and we should embrace it. And if we added a long-term cap for the total supply, it would be even easier to accept it.