Bitcoin with primitive Blockchain Currently Bitcoin blocks are limited to 1MB and each block seems to hold roughly 1000 transactions assuming each transaction is 1KB.

Much of a transactions size seems to be caused by Bitcoin's built-in scripting system to facilitate complex transactions.

Would Bitcoin benefit from a deliberately primitive blockchain, one that can only records the input addresses and output addresses?

My thinking is that for most transactions you would only need 1 input and 2 outputs. So you could reduce the transaction size from 1KB to about 100 bytes. That would increase Bitcoin's Tx/s by 10 times I'm assuming.

What's more, since the Blockchain is primitive by design it couldn't handle anything like Escrow or any other kind of transactions. This would encourage people to do those activities before they record their transaction on the Blockchain which would mean there would be less demand on the Blockchain for transactions.

These are just ideas I had, if anyone could disprove them that would be cool too!
I won't go into details of segwit, which in fact allows for bigger blocksize than 1 MB... sticking to your approach:


  Much of a transactions size seems to be caused by Bitcoin's built-in
  scripting system to facilitate complex transactions.


no, not really to facilitate complex tx. It is required for every tx. The logic is to sign a tx, with an output condition. The signature proofs, that data hasn't changed during transfer to the blockchain. When the receiver decides later on to spend the tx, he needs to proof, he has the privkey for the pubkey hash of the previous tx. As a hash function is a one way (as per todays knowledge), this proofs, that he is indeed holding the priv key for this pubkey hash, and as such can spend the funds. 

If you take this functionality out of blockchain, then you have a normal ledger, that can be manipulated by the owner of the ledger (aka as it is today with non-crypto financial institutions). This would mean, no need for a blockchain... 

Btw: a minimum tx is somewhere around 227 bytes. 

The logic is defined at several places, good reading is here:

1.) bitcoin.org - the developper section

2.) the book from Andreas "Mastering Bitcoin" - it is online available

3.) http://www.righto.com/2014/02/bitcoins-hard-way-using-raw-bitcoin.html