How does the mining process support the currency? Why is mining Bitcoins necessary? Is it essentially a distribution mechanism to ensure Bitcoins are not held by a few (wealthy) individuals from the get-go who might just hoard Bitcoins rather than be encouraged to spend them? 

Isn't the (growing) expense of mining Bitcoins going to have this effect in any case - specialist Bitcoin mining companies (with racks of expensive hardware) could effectively make it impossible for anyone else to mine Bitcoins - meaning the currency cannot filter down evenly through the network but ends up congealing around power users...
Mining is not just a way to ensure the initial distribution of bitcoins. It happens that coins have been distributed through mining, because it was easy and useful to do it this way, so this might be a bit misleading, but mining will remain essential even after all the bitcoins (~21MBTC) have been distributed.

Mining has not been designed to distribute coins. It's exactly the opposite: coins are distributed to attract miners. The network needs them.

Mining is the core mechanism that makes Bitcoin possible. 
The bitcoin block chain (i.e. transaction history) needs to be updated continuously. In effect, one block is added to the chain about every 10 minutes. Mining is the little miracle that allows trust in the network as a whole, without trusting any single participant¹. The idea is to add some artificial difficulty to block creation, so that only a few blocks are presented to the network for consideration (and for validity checking). This way, the network can choose which block will be accepted as the next reference, while nobody has full control on block creation.

The hard work of miners that build those blocks must be compensated (hardware equipment and electricity are not cheap). A reward has therefore been included in newly created blocks. For now, the reward is constituted mostly by newly minted coins. But given that the mining process is essential to the bitcoin ecosystem, that reward must (and “hopefully” will) be replaced by fees, paid by transactors, when coin creation is going stop completely, in about 130 years.

—

1. Assuming no one has access to more than 50% of the total computation power of the network.