The reason is that otherwise you just end up playing a game where the really large entity files a bunch of motions you have to reply to, and your lawyer starts billing you in the 5-6 digits before you've even had a chance to make your case to the judge. For most individuals (or even small companies) this might cancel out whatever you are trying to accomplish with your lawsuit.
It also means that you are able to handle the issue from home, possibly from your house, without having to deal with a lawyer in the Delaware (PayPal) or California (Instagram), and you can do this without having to first have a complex battle over where the jurisdiction of your argument is (something a friend of mine is going through right now).
Meanwhile, both Instagram and PayPal continue to allow you to use small claims court to file smaller issues. With PayPal, as they are in Delaware, that is for claims up to $15k, which is more than most individuals keep in their PayPal accounts, and for Instagram (in California) that is $7.5k (although I'm not certain what to compare this against, as I'm not certain what people would ask for when they sue).
Additionally, it actually offers you protections: in both the PayPal and Instagram versions of the clause, they are subject to the same arbitration requirements that you are; the alternative is that they can just decide to start a complex legal issue with you, causing all of the aforementioned costs and complications, even if they doubt they'll be able to win (but, of course, do think they could convince the judge to not throw it out of court; although even asking the judge to do that might be costly for you).
(edit) Woah... except that Instagram actually has exceptions to the arbitration clause, which give them some things they can still sue you over (such as API misuse and network intrusion). (I am fairly confident the PayPal one did not; I had a lawyer review it, and that did not come up, and I actually read that one thoroughly.) That is really lame. :( That said, issues involving your IP (including trademarks and copyrights, such as on your photos) are not subject to this clause either. (/edit)
The downside people often cite is an inability to participate in class-action lawsuits, but individual players in such deals really don't get anything out of it: the main reason you should then care is if you feel the need to make a philosophical point that class actions should happen because they are a way to keep large entities with distributed customers in check; to note: I totally appreciate that stance.
That is important enough that I will repeat it: I totally understand that someone would then decide that they don't care about the earlier stated benefits (which, to be clear, after my comments on this related to PayPal, I ended up seeking real legal advice on from my corporate lawyer, and he actually came up with those same reasons) and thereby would decide to opt out anyway. However, a lot of people seem to have knee-jerk reactions to the "arbitration" part, and that can be a benefit.
(The downsides were that it might take a few more days if you are trying to get injunctive relief--such as forcing PayPal to immediately reactivate your account so you can continue your business ASAP while you resolve the issue--and that you would probably not be able to appeal the decision if you didn't like the outcome.)
(I will then say that the result, in my situation for the PayPal arbitration clause, ended up being a semi-tentative "ok, let's opt out"; however, it should be noted that I move millions of dollars through my account annually, have a business model where I'm forced to keep many hundreds of thousands of dollars in my account at almost all times, and at this time do not have an alternative way to cheaply and automatically pay international vendors small quantities of money, so I'm overly reliant on them.)
Arbitration is really only fair and effective between equal peers that can choose to split the costs of the arbitration, and agree upon an arbitrator together.
In cases of arbitration between a large entity and a single small customer, the large entity wins virtually every single time. The top 10 arbitration firms in the USA only rule in the favor of the consumer/employee 1.6% of the time [1]
There's not a single health plan available in many states that does not require agreeing to binding arbitration for coverage. None of them allow you to opt out, even if you're willing to pay more. Sign away your right to sue, or no coverage for you. Consider that under health care reform, one is required to purchase one of these plans. There are dozens of industries that are like this, where it is virtually impossible to receive a service or a good of that class without agreeing to mandatory binding arbitration, such as residential ISPs.
Add into the fact there is almost no way to appeal decisions, make no mistake, Instagram is not doing this for your benefit.
The term "kangaroo court" comes to mind.
[1] http://consumerist.com/2007/07/26/support-the-arbitration-fa...
That said, PayPal and Instagram both choose AAA (American Association of Arbiters), which honestly seems to be sufficiently large as to not be concerned about bothering anyone. FWIW, my lawyer seemed to believe they would be fair if I ever needed to arbitrate with PayPal: them being PayPal-biased was not a concern.
As for the low rate... I would have expected that... wouldn't you have? With an arbitration clause in place that allows you to initiate and complete a complaint from your home over the phone, one would expect to suddenly get many more complaints than requiring users to actually sue you. Most users really do have ludicrous expectations or misunderstandings, and probably go to arbitration over tons of things that have nothing at all to do with the business they think they are bothered with.
Blocking class action suits is indeed the point of these arbitration clauses, and it's a bigger problem then you make it out to be. What class action suits deal with is the basic problem that it's easy to steal a little bit of money from a lot of people because no individual will find it worth their while to enforce their rights. Without class action suits, it's always profitable to steal from people so long as you don't steal enough from any one person for it to be worth litigating.
What happened to the open-web??
(Or went evil, YMMV)
Money and lawyers :P