Hashing the block chain?

So, the asic resistant or fpga resistant coins have been the buzzword for the last couple years. Most of these coins rely on a new, asic resistant algorithms. My question / suggestion is: "why not start up a sha2-256 or a sha3-whatever block chain where hashing must be done to the whole block chain, not just the last block. The goal is to make hashing algorithm require say 32GB of RAM... eventually...

Here is an example spec:
1. DEFINE block chain - a collection of blocks" such that SHA3-512 (or some other hashing algo) hash of "Large chain - defined below" is equal to predetermined value up to X characters. X will determine the difficulty.
2. DEFINE block - a set of transactions concatenated with a string of Y characters called pad.
3. DEFINE Large chain - a concatenation and predefined mixture of copies of block chain such that length of large chain >= 32GB (eventually).
4. Criteria - Block B can be added to block chain if the hash for the Large chain is equal to predefined value up to X characters.

The goal here is to make the memory requirement for 1 hashing operation to start up as a reasonably low number but grow with the size of the block chain, say up to 32GB. The 32GB memory requirement per calculation will push ASICS, FPGAs and GPUs out of the pool of available resources once the block chain gets big enough.

The rules for defining large chain can be set such that memory requirement to execute 1 hash instance scales by the size of the chain.
1. initial memory req <1MB (FPGA friendly)
2. 2nd stage memory req >1MB and less than 1GB (GPU friendly)
3. Final memory req = 32GB (CPU only)

What do you guys think?
I think allot of original bitcoin code for SHA2-256 can be leveraged also opening the pool to existing fpga, asic and GPU miners, but then slowly weeding them out as block chain grows. This will ultimately make it very expansive for any one organization to assemble large sets of ASICS and possibly controlling or forking the chain. No one is going to build a new ASIC mining center that will become outdated before hardware can pay for itself. Although some may shift existing ASIC FPGA hardware to this block chain if SHA2-256 algo is selected for it....