Why is there no plural indefinite article?

In most languages indefinite articles stem from that language's word for one. For instance in French un, or in German ein, In Italian and Spanish uno or in Portuguese um.

English is no exception: an was derived from one. Note that an was the original indefinite article; the shorter a came later when the final "n" was dropped before consonants.

In some of the languages I mentioned above, the plural form of the indefinite articles is simply formed by applying the noun plural inflection: unos/unas or uns/umas.

In others, such as German and Italian, there is no plural form to the indefinite article. Italian use the partitive article degli/delle as a substitute and this is probably also the origin of the French plural form des.

For some reason English did not go through this last step either. To understand why we need to go back to the way Old English solved the problem.

In Old English adjectives have a different declension depending on whether the noun they qualify is determined or not.

"The glad man" reads

se glæd guma

whereas, "a happy man" is:

glæda guma

As one can see, only the adjective changes.
For one given adjective, you could therefore have different inflections depending on:
- the noun gender (masculine, feminine, neuter)
- the noun being singular or plural
- the four cases (nominative, accusative, genitive, dative)
- whether the reference is definite or indefinite.
So that the same adjective would have to follow either the "definite" declension or one of three "indefinite" declensions.

þa glædan guman

Edit
<conjecture>
The theory I'm trying to check (community please feel free to edit) is that in various languages (Icelandic for a language very close to Old English or Romanian) the article is added as a suffix to the noun. Then it often "detaches" and passes in front of the noun. Icelandic is half way through for the definite article in that matter.

As for the Old English indefinite article, my conjecture is that the process never went through for a number of possible reasons:
- The "loss of inflection" of early Middle English won the race
- The plural of "an" was not easy to evolve at that time (the Romance "-s" plural had not imposed itself yet).
</conjecture>

But the need is still there, just as in any other language where a specific word emerged for the plural indefinite article. This gap is filled by placeholders such as some or a number of.

Most linguist agree that Proto Indo European did not use articles. Latin does not have any kind of article, and Ancient Greek arguably had no indefinite article either - it was using something very much like present-day English some (τις - "a certain"). And I believe that Old German did not have any article either.

It is a very remarkable fact that articles appeared in many modern Indo European languages in a largely mutually independent yet very similar manner. My feeling is that their emergence compensates for the gradual loss of inflection in these languages. But then present-day German is a powerful counterexample...

As pointed out elsewhere, language is the result of an evolutionary process, not logical design.

The origins of the word "the" aren't connected with those of "a/an", so there's no reason why they should share all characteristics.

As OP says, "some" can function as a kind of 'plural' for "a/an". So can "a few", "a number of", etc. In some contexts, "any" can be used as the pluralised version of "a/an". I'm not overly concerned about the scope of the term "indefinite article" – it's just a (sometimes enlightening) name we often use, not a 'pre-existing' class into which any given word either falls or doesn't.

It's not as if our language is seriously restricted by not allowing for "a/an" to be used of multiple subjects. And after all, in some contexts "a" can effectively refer to multiple subjects where "the" implies a single one...

"A president should be allowed to say he 'screwed up', surely?"

"I'm not talking about a president, the president shouldn't have said that!"

LATER: More specifically addressing OP's question as to why "a/an" can't be pluralised the same as "the". Firstly, note that in the above example, "a" is effectively pluralised – as becomes clear when you realise it means "presidents in general" rather than "a randomly selected president".

Secondly, consider "Recipe: Mix some cloves, a cinnamon stick, and apples in a bowl". There's no need for an article when we pluralise "an apple" there.

Thirdly, as @Robusto implies, some/many/most/all contexts where you would use the indefinite article in reference to "one of it" simply don't lead to meaningful contexts if there is more than one of it.

Fourthly, "a" can mean exactly "one", particularly in contexts associated with 'countability' (so can "the", but more in the context of 'identification'). This makes us leery of using it around plural subjects, because we sense it sits uneasily with 'one-ness' of "a".

When you are referring to a specific item or specific items, you use "the", like

I have the steak.

or

I have the steaks.

When you are referring to a "nonspecific" item, you use "a" for the singular, like

I have a steak.

If you were to leave out "a", you would get

I have steak.

How many steaks do you have? One massive steak? Two steaks? Exactly π steaks? 4/5 of a steak? Without the article, "steak" in this example becomes a "non-counted" entity; you aren't indicating anything about whether there are discrete items. In

I have a steak.

you are referring to a collection of discrete items. When you say

I have steaks.

though, it is clear that you are referring to discrete items. If "steaks" is plural, you have to be able to count them and therefore have to have more than one discrete item. The article isn't necessary. However, you can say

I have some steaks.

According to the Wikipedia entry for "article (grammar)", "The articles in the English language are the and a/an, and (in some contexts) some." (emphasis added) In the case of talking about "indefinite objects", the article isn't needed to show that you are talking about discrete items or specific items.

I realize that some is an effective substitute for plural a, but in that case, why is it not considered to be an indefinite article?

Because in English the indefinite articles are an and a; some, a, an, the, and other words are classified as determiners.
It just a matter of classification; for example, the NOAD copy that comes with Mac OS X 10.6 ("New Oxford American Dictionary 2nd edition © 2005 by Oxford University Press, Inc.") classifies a and the as adjectives.

a /eɪ/ (an before a vowel sound) [called the indefinite article]
adjective
1. used when referring to someone or something for the first time in a text or conversation: "a man came out of the room"; "it has been an honor to have you"; "we need people with a knowledge of languages."

the /ði/ /ð(ə)/ /ði/ [called the definite article]
adjective
1. denoting one or more people or things already mentioned or assumed to be common knowledge: "what's the matter?"; "call the doctor"; "the phone rang."

The NOAD that comes with the Mac OS X 10.7 ("New Oxford American Dictionary 3rd edition © 2010 by Oxford University Press, Inc.") defines the articles as determiners.