As a newcomer to Bitcoin Core.
Welcome.
I find the Bitcoin Core blockchain impossible to download now,
You may want to consider a lightweight wallet if your computer specs are not modern enough to handle it.
it is growing exponentially
It is not growing exponentially. It is growing linearly.
and is just too slow
You'll find that a modern computer with enough RAM and an SSD will help a lot.
and too big for the average person.
It is currently less than 157 gigabytes.
An "average person" can purchase a 256
gigabyte SD Card for less than $25 at Amazon.com:
http://a.co/7Wu4ib4An "average person" can purchase a 1
terabyte external SSD drive for less than $350 at Amazon.com:
http://a.co/6TtcGMxAn average person can also run Bitcoin Core in "pruning mode", since the "average person" doesn't have any personal need to store the blockchain.
What's the point?
The point to running Bitcoin Core? There may not be one. That's for each user to decide for themselves. You could establish an account with a service such as Coinbase, you could run a lightweight wallet such as Electrum, you could run Core with pruning. Each user can decide for themselves what best fits their needs.
I wanted to have the entire blockchain on my computer,
Why?
but it ain't happening.
That's ok. If you can't store the blockchain, then others will.
1) Bitcoin has been in existance for almost 10 years. But 50% of the entire blockchain is just from the last year or so!
You may want to check your math on that.
Blockchain size a year ago was just a bit more than 102 gigabytes.
(157 - 102) / 157 = 35.03%
That's a LOT less than 50%
I mean, I'm at 30% downloaded right now, and that's right up until November 2015!
Correct. The blocks were not full the first 6 or 7 years of Bitcoin's existence. There just weren't many people using it yet.
2) If your hard drive screws up, you're screwed! I was three weeks into the Bitcoin Core blockchain download, made it to 90%. Then, BAM! My hard drive died. Got a new drive, decided to try again.
I create regular backups of data that is important to me. That way I don't lose it when my hard drive "screws up". You may want to try doing that. You can recover a backup of your hard drive, and then just pick up where you left off.
Seems slower than ever, my computer runs to a crawl at times.
If it is slower now than before purchasing the new drive, then I'm guessing you purchased a drive with lesser specifications. Perhaps purchase storage with the same OR BETTER specs next time?
3) Even if someday I do manage to catch up to the most current block/day, I believe soon if not yet already there, we will never be able to get past a certain percentage, say 98%, due to the ever-growing nature of the blockchain. It will get to the point where it is growing faster than than possible to download.
The block chain grows at a maximum average rate of 4 megabytes every 10 minutes. If your internet is incapable up supplying 4 megabytes every 10 minutes (that's less than a 56k dial-up modem) or your computer is incapable of processing 4 megabytes every 10 minutes, then you should probably not be trying to run Bitcoin Core.
4) Bitcoin is not new-user friendly! Basically, if you missed this boat, the only other one to hop on are the life rafts (exchanges) circling around the boat like a body of sharks. Anyone that the blockchain download after 2016 I bet put in a lot of wasted time and resources trying.
I started up a new node recently. It took less than 5 days for me to get completely caught up.
5) Windows automatic updates really, really screw things up. With Bitcoin Core download, there is no time that your computer is idle for the updates, yet Windows thinks it is. So it kills the process with the reboot.
Windows is crap. That's not Bitcoin's fault. Windows will screw up a lot of things. Sounds like a good reason not to use Windows. However, if you feel you need to use Windows, then I recommend frequent backups so you can recover from any mess it makes.
6) Actually, any sort of blip whatsoever in your Bitcoin Core client or storage device causes havoc. Its not like a few years ago, where you're looking at 20 gigs. We're dealing with over 100 gigs now.
As I said, modern computer with good internet, or lots of patience and good backups, or choose something other than Core.
What happens when this reaches a terabyte? Not too far off, watch.
At a MAXIMUM possible growth of 4 megabytes per block, a terabyte is nearly 5 years away. At a TYPICAL growth of 2.5 megabytes per block, a terabyte is more than 7.5 years away.
So, although it is enticing to attempt having the entire blockchain for failsafe transactions, it simply isn't feasible anymore.
You don't need to store the entire blockchain. You can run Core in pruning mode and your transactions will be just as secure.
What happens now?
People that are able to run Core will. Those that are not able to, won't.
Well, one could say Bitcoin should just adapt permament light wallets ala Electrum using multiple redundent cloud-based storage for the blockchain.
Electrum is a very good option.
I've mentioned other options earlier in this post.
Question is, who pays for it?
That depends on the software you use.
Easy. Have silicon-based chip storage, with a percentage coming off transaction fees for the maintenance. Except then you have individual governance, which does not work with the Bitcoin system.
Bitcoin is working just fine the way it is. I'm not even sure what you're trying to suggest here.