The flipside is that there are a surprising number of organizations with lots of money that haven't figured out a better way of distributing it, so applications can still be a good way of getting funds. One of my acquaintances, for example, just got $100k in seed funding (with no equity in return) entirely based on a 15-page application sent to a funding body, having had no previous contact with the funder.
Having painstakingly gone through the process of writing 35 page Grant Proposals for a hospital and getting funding from the government on all three occasions, I can assure you that the application process was just a formality and legal requirement.
The funding came through because the grantor had a relationship with the department heads that received the funds.
Obviously, you need to meet the required criteria, and a perfectly crafted application is a requirement, but all things being equal it boils down to relationships.
I've also done that several times; it really depends on the funder. In a surprising number of cases, the funder has wound up with a pile of money and not enough contacts with relevant people, so they really do choose people out of the applicant pool. It can also vary by country. In Europe, for example, how much relationships matter seems to vary north-to-south. In southern Europe it is pretty much 100% about relationships.
Perhaps in reaction to what's perceived as southern-European corruption, in Scandinavia there is substantial pressure on funders to make their decisions based on the official application process. There's a worry that "contacts" means your old grad-school buddy, someone you know from a sports club or weekly board-game get-together, etc., as opposed to scientific merit. There's also (what seems to me, as a foreigner) a strong worry that the process shouldn't be perceived as a sham, which means that at least some proportion of the funds have to be doled out according to the official application route, to prove to everyone that the system works like it says it does. In practice that ethos is upheld at some places more than others, of course, but in some circumstances you really can just apply and get money.
The government most likely. There are several places in this world where startups, and businesses in general, almost drown in free money like this. The downside to this is that in order to get this free money, you first have to go through a senseless amount of paperwork, bureaucracy and bullshit. But, to be honest, it's a small price to pay for what you get.
Northern Ireland for example is a startup paradise. InvestNI, the government body in charge of giving away free money, recently had to give back a whooping £39m (that's $62m!) because it couldn't find enough businesses to give the money to quickly enough.
Sadly, many entrepreneurs in these places have never experienced what doing a startup in the "real-world" is like and they don't realise what an incredibly competitive advantage these grants give them. So instead of leveraging this opportunity, many spend most of their time whining and complaining about the paperwork and bureaucracy involved.
Northern Ireland for example is a startup paradise.
I can confirm this. One of the guys on my team has contacts in InvestNI and I'm told that they want and need to give money away or else they won't get as much for their budget next year, so its really easy to get free money off them.
In the case of my country's government (or Chile's), you can get a grant for your startup without having prior contact.
However, in my country at least, I do know they give more weight to applications from people they know (I don't know how, the others might get processed later or whatever, or they skew in their favor).
So, you might get funded without contacts, but it's less likely (I guess you have to be outstanding in some sense, either killer business plan or credentials).
For example, I don't think of YC as a way of getting funding, but as a way of getting things done well, thank to the possibly unbeatable amount of white board advice from so many good people that it's very hard to get otherwise.
You can have a great idea, have a great team and even have good money, but you could still make a mistake in choosing one of the key strategies of your product.
I, for example, think that YC is perfect at trying to avoid making this kind of mistakes and helping you make your idea stronger.
