user18196: 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() <= 100 (source)  
The scriptSig is not too small. vin[0].scriptSig.size() >= 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.

user21052: 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.


18196: <p>There are a few limitations on the structure of the coinbase (reward) transaction in a block. </p>

<ol>
<li>There is only one input. <code>vin.size() == 1</code> (<a href="https://github.com/bitcoin/bitcoin/blob/v0.10.0rc3/src/primitives/transaction.h#L232" rel="noreferrer">source</a>)</li>
<li>It doesn't reference any previous output. <code>vin[0].prevout.IsNull()</code> (<a href="https://github.com/bitcoin/bitcoin/blob/v0.10.0rc3/src/primitives/transaction.h#L232" rel="noreferrer">source</a>)</li>
<li>The scriptSig is not too big. <code>vin[0].scriptSig.size() &lt;= 100</code> (<a href="https://github.com/bitcoin/bitcoin/blob/v0.10.0rc3/src/main.cpp#L876" rel="noreferrer">source</a>)  </li>
<li>The scriptSig is not too small. <code>vin[0].scriptSig.size() &gt;= 2</code> (<a href="https://github.com/bitcoin/bitcoin/blob/v0.10.0rc3/src/main.cpp#L876" rel="noreferrer">source</a>)   </li>
</ol>

<p>I don't see the point of any of these. #1 and #2 enable <a href="https://github.com/bitcoin/bips/blob/master/bip-0034.mediawiki" rel="noreferrer">BIP34</a>, 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.</p>

<p>Why isn't a coinbase transaction just a transaction which:</p>

<ol>
<li>Has at least one input that doesn't reference any previous outputs (for use in <a href="https://github.com/bitcoin/bips/blob/master/bip-0034.mediawiki" rel="noreferrer">BIP34</a>)</li>
<li>Allowed to claim up to (block reward + fees) more than it can spend</li>
</ol>

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

<p>I know for Bitcoin it's likely too late for these to change. <strong>Is this a case of over-designing, or are there security reasons for any of these constraints on the coinbase?</strong> 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.</p>
 21052: <p>The correct answer is: ask Satoshi.</p>

<p>My guessed answers to the questions you asked:</p>

<ol>
<li><p><strong>Why only one input?</strong> 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.</p></li>
<li><p><strong>Why reference a null <a href="https://bitcoin.org/en/developer-reference#outpoint" rel="nofollow noreferrer">outpoint</a>?</strong> 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.</p></li>
<li><p><strong>Why limit coinbase size to 100 bytes?</strong> 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.</p></li>
<li><p><strong>Why specify minimum coinbase size as 2 bytes?</strong> Highly speculative here, but maybe Satoshi foresaw the easy-duplication-of-coinbases described in <a href="https://github.com/bitcoin/bips/blob/master/bip-0030.mediawiki" rel="nofollow noreferrer">BIP30</a> and wanted to require people use something like the <a href="https://bitcoin.stackexchange.com/questions/32603/why-didnt-satoshi-make-the-nonce-space-larger/32618#32618">original extranonce</a> to help prevent accidental TXID collisions.</p></li>
</ol>
