I didn't say it should not, I said that its not supposed to, which I suppose is not the best way to convey my thoughts. Intended is probably a better word to use.
That still leaves the question though. What makes you think that the Chain Pact was not intended to have access to Eldritch Blast? I think they would have made it a Tome-specific feature, or Invocation, if it was intended only for Tome.
I think it is more likely that EB held an important place in the past versions of the class, and as a result was made relevant in this version as well. Unfortunately, A lot of Optimizer types latched onto that as the only acceptable way to Warlock. In my homebrew document, it will be an invocation that can be grabbed by any Warlock, but will not have the bonus invocations that are made for it (Agonizing Blast, Eldritch Spear, the UA ones).