That's the one issue I had too. I still have early adopter customers of mine who pay me $6 a month (minimum now is 4x that), and I'd never dare to change their original pricing.
I don't know, is it really that much of an issue? I mean, you paid a reduced price for using the service early--albeit it would have been buggier, you're contributing useful feedback, etc., but you obviously were deriving a benefit from the service so it was a fair trade. Fast forward, the product is more mature and "better", is it that unreasonable to ask you to pay more after 6 months of getting to use the better product at the better early adopter rate? And that's the deal killer for you?
[note: I have nothing to do whatsoever with Intercom, just my 2 cents]
Case in point, we sell our product for $99/year with a $20/month add-on. Some people got this for $39-$79 for life, and I'll never change that because I wouldn't have a product if not for their early support.
I'll also never ask our current customers to pay more, provided they stay active.
The overhead of keeping early adopters alive at initial prices is not significant, so there is very little risk in grandfathering them in. However, raising the price risks driving brand advocates (like those commenting here) away, or at best, making them disgruntled.