Strings do not have known keys associated with their indexes

TypeScript Version: Nightly

Code

{
    const t: 't' = ("test" as const)[0];
}
{
    const t: 't' = ([ 't', 'e', 's', 't' ] as const)[0];
}

Expected behavior:

TypeScript associated keys with values for string literals.

Actual behavior:

TypeScript gives all indexes into a string the type string.
TypeScript allows out of bounds indexes into string literals.

Playground Link: https://www.typescriptlang.org/play?esModuleInterop=false&experimentalDecorators=false&emitDecoratorMetadata=false&ts=4.1.0-insiders.20201010#code/PTAEBcFMGdwLlAIirRBuCBPADpAJqAIbSgDukANhUSdgPbTQCWARhZKEwHagAqAygBpQAYzoBbbOygVMnceICu4Qmw6EuBANZc6pHoXCiJ2JuwhNxkAFBiusCDCMBeJCnCIax++DTXrIKDQABZ0ihQELByQAI6KTABuhOxcRuB0oAAUAE6QhHh0XLKgANqgAOTg5cLlkNUV0PWV5aAAugCU-nYO8BVVoK7uJQAMrX62hdB07AB0FHQA5pkuzq7N7RiBAGbJ0JDCduDZhNly6WTBhnz8oFEUTJAJMF2TRiKX2Qiw2dwLA46wEoAVjGL3s00gc0WyxwkDoW1EHwGqyQ31+iA2oG2u323iOJzOGVIlyMAlulAeT2g-gA3tZQAzvD0nP8ys0anUao0av1Wl5ur5-IymWkEM1-kNRn4AL5AA

Related Issues: https://github.com/microsoft/TypeScript/pull/19846

Strings, especially string literals, ought to be comparable to an array of characters when indexed.
When accessing a string "foo" the type should be comparable to indexing readonly [ 'f', 'o', 'o' ], especially considering that JavaScript strings are completely immutable.

I doubt anyone would be against the lengths being known too, ex: const length: 4 = "test".length;

Start with the linked TypeScript Playground reproduction and compare string indexing with the readonly tuple example. The requested behavior is for literal string indexes to produce character literal types, reject out-of-bounds indexes, and potentially infer literal lengths; the issue names no source files or tests.