Why bother having limitations on Bitcoin Coinbase Transaction Scriptsigs? There are a few limitations on the structure of the coinbase (reward) transaction in a block. 


There is only one input. vin.size() == 1 (source)
It doesn't reference any previous output. vin[0].prevout.IsNull() (source)
The scriptSig is not too big. vin[0].scriptSig.size() &lt;= 100 (source)  
The scriptSig is not too small. vin[0].scriptSig.size() &gt;= 2 (source)   


I don't see the point of any of these. #1 and #2 enable BIP34, but they are not necessary to achieve the same outcome. The size constraints don't really limit anything, if a miner wants to make a large block they can just many many outputs in their coinbase, or many many transactions into their block.

Why isn't a coinbase transaction just a transaction which:


Has at least one input that doesn't reference any previous outputs (for use in BIP34)
Allowed to claim up to (block reward + fees) more than it can spend


In particular, the coinbase could optionally have further null inputs and could spend previous outputs. 

I know for Bitcoin it's likely too late for these to change. Is this a case of over-designing, or are there security reasons for any of these constraints on the coinbase? Loosening constraint #2, in particular, makes me pause because of a bitcoin development mailing list email concerning how allowing the coinbase to spend prevouts would enable securely paying a miner to mine a chain reorganization in a particular way.
The correct answer is: ask Satoshi.

My guessed answers to the questions you asked:


Why only one input? You can't predict when a particular coinbase transaction will make it into a successful block and you can't spend the output of a coinbase transaction for 100 blocks.  That means using a regular transaction is much superior for any normal spending.  If there's no normal case for adding inputs to a coinbase, maybe Satoshi thought it best to disallow inputs to prevent un-thought-of attacks.
Why reference a null outpoint? Using the same basic format as a regular transaction probably allowed code reuse.  If he had optimized the coinbase, we would've saved 36 bytes times 338,692 blocks (so far), or about 12 MB.  Not a big deal.
Why limit coinbase size to 100 bytes? We know Satoshi used the coinbase to put a message in block 0.  Maybe a 100-byte limit was his attempt to prevent anyone else from using that same mechanism to add overlong messages.  This was probably quite smart: from the fairly early days through today, many miners add messages to all of their coinbases---we can only imagine how annoying and wasteful those messages would be if they weren't limited to 100 bytes.
Why specify minimum coinbase size as 2 bytes? Highly speculative here, but maybe Satoshi foresaw the easy-duplication-of-coinbases described in BIP30 and wanted to require people use something like the original extranonce to help prevent accidental TXID collisions.