Why is an initiator tRNA required, distinct from the methionine tRNA used in elongation?
I think the key to understanding this is to appreciate how different the initiation process is from the rest of translation. 

The 30S ribosomal subunit recognises start codons via an interaction with the Shine-Dalgarno sequence that lies upstream in the mRNA. The remaining steps of initiation involve recruiting fMet-tRNA and, critically, placing it into the P site of the ribosome. In contrast, during elongation, aminoacyl tRNAs enter at the A site before their amino acid cargo is joined to the growing polypeptide which is held in the P site as a peptidyl tRNA. So you can see that the initiation process is special because of the need to prime the whole translation process by placing the first 'peptidyl' tRNA (actually N-formylmethionyl tRNA) into the P site. 

There are two tRNAs for methionine, tRNAfMet and tRNAMet, and only the former is a substrate for the enzyme methionyl-tRNA formyltransferase. This effectively partitions the supply of methionine into two separate pools, one for use in initiation and one for use in elongation. In fact you could argue that initiation involves a different amino acid (N-formylmethionine) which is also coded by AUG.

Since an N-formylmethionine is essential for initiation, the simplest alternative would be to have a situation where a single species of methionyl-tRNA was a substrate for the transformylase. This would mean that N-formylmethionine would have to be allowed into the A site, and all those formyl groups would have to be subsequently removed from the internal methionines. 

Update in response to comment from the OP

Having re-read the original question, I can see that I jumped the gun and actually answered a different question. The real question is much deeper. 

Firstly, although the details differ, both bacteria and eukaryotes feed methionine through separate pathways for initiation and elongation.  Bacteria are discussed above; eukaryotes channel methionine through two different pools of tRNA, tRNAiMet and tRNAMet. Clearly this channelling is a universal feature of translation systems.

Next, let's look at tRNAMet abundances in E. coli. Since all protein-coding genes have a single start codon and, on average, a few internal methionine codons, we might anticipate that there would be more tRNAMet than tRNAfMet. But this isn't the case: according to Dong et al 1996 tRNAfMet is present at around 3x the level of the elongation species. 

This suggests to me that there is something inherent to initiation that requires a higher level of the corresponding methionyl tRNA. Now you might say that this discrepancy is rather small but bear in mind that one of the properties of Met-tRNAfMet is that is easily rejected by elongation factors (reference). This is important because any charged tRNA can enter the A site before being compared to the current codon. By being easily recognised as 'wrong' for elongation, Met-tRNAfMet is, to some extent, excluded from the elongation process.

So far I have presented facts -  what follows are my own ideas.
If a single Met-tRNA species was used both for elongation and for initiation it would have to optimised for entry into the elongation process, spending time interacting with ribosomal  A sites. In order to maintain the level of free Met-tRNA required to drive initiation I conclude that much higher levels of this single Met-tRNA would therefore be needed. This in turn would increase the transient entry of this species into all A sites, and it would essentially act as an inhibitor of elongation.