Why limit it to bitcoin businesses?
Somebody should create a website where you can get a few bitcoins for free, to subsidize adoption.
You mean give a significant amount of bitcoins to the 'important' businesses?
Who decides which are 'important' ?
How do you make sure somebody isn't creating fake businesses just to get free bitcoins ?
If you want to subsidize bitcoin businesses and have answers to those questions, then I heartily encourage you to go for it!
A. Gavin points out an important reason for opposition to subsidies. Subsidies require an individual or small group to exercise arbitrary power (e.g. pre-mine 3 million coins and slowly dole them out to whichever businesses seem likely to make a large contribution). The individual or group would need to actively screen businesses to make sure that they are legit (e.g. order from them, solicit reviews from trusted sources, etc.). I can see that many people take a negative view of arbitrary, command economy-style arrangements like this. I think these kind of interventions are necessary to ensure a good equilibrium outcome.
B. Gavin asks: Why not just subsidize everyone via the faucet?
My answer: One should do this. However, faucet subsidies are not enough. Consumer subsidies and merchant subsidies are complements rather than substitutes.
Subsidies for Merchants
M1) 10 BTC/day drips to merchant conditional on his maintenance of an attractive BTC storefront
[this subsidy increases the supply of attractive BTC storefronts. The subsidy differs from a consumer subsidy because it is larger and you need to have a store open to be eligible to receive it.]
Subsidies for Consumers
C1) 1 BTC drops from faucet into wallet of Consumer A
C2) Consumer A decides to either a) trade 1 BTC for goods b) trade 1 BTC for USD c) hold on to 1 BTC for speculative purposes
If Consumer A makes choice (C2a), then faucet subsidies encourage merchants to supply BTC goods and services. That's great! If Consumer A chooses (C2b) or (C2c), then faucet money will leak out and fail to encourage merchants to supply anything. That sucks! However, one can intervene to make the faucet subsidy more effective. If more merchants are subsidized, then more attractive storefronts will exist and consumers will be more likely to choose C2a. Accordingly, the provision of merchant subsidies makes faucet-style subsidies more effective. This is why merchant and consumer subsidies are complements rather than substitutes.
For a mathematics/statistics heavy exposition, which explains why merchants should probably get the lion's share of the money, you can look at the paper I linked to above. It is about ACH banking transfers, but the principles are applicable to bitcoin.