Your proposal seems to lack a number of details necessary to really evaluate it.

I am assuming for the sake of discussion that these 'mini blocks' are considered equivalent to a 'big block' as regards their canonical status within the chain. That is, they would build upon previous blocks and be built upon, they would be considered as 'one confirmation', and so on.

Block 100 may reward 25BTC, block 101 may reward tx fees of 0.25BTC, block 102 tx fees of 0.3BTC, block 103 25BTC, and so on.

First of all, they would necessarily have to use a different algorithm than the big blocks. Otherwise the big miners would simply mine them as well. The competitive process of mining results in those who have the most efficient (GH/J or ultimately GH/$ i.e. low cost of energy region) hardware outcompeting others.

To illustrate this clearly with arbitrary numbers. Assume 1BTC is worth a bit less than $1000 for the sake of simplicity.
I am a miner - I would, disregarding risk, be willing to spend around $25000 to mine a 25BTC block.
For a 'tx fee' block, let's say it contains 0.25BTC - I would therefore be willing to spend around $250. I think this should be apparent.

A proper mining operation (latest hardware, or located in a cheap energy region, etc) will be able to produce more hashpower for that $250 and hence outcompete all others. edit: Assumption being that there is no reason other than goodwill or anonymity for someone to spend >$250 incl all overheads to mine $250 worth of BTC)

So it must be based on a different algorithm for that reason.

It must also be based on a different algorithm for the following reason - it is hugely problematic for the network to have 'easy/low reward blocks' that could be misconstrued by users as representing a full confirmation. It would be utterly trivial for someone to 51% attack the 'mini chain' if it shared an algorithm with the main chain.

There are other issues floating around in my head right now (if the blocks are not more difficult, but still have canonical status within the chain, they weaken it rather than strengthening it due to the ease of attack) but I don't really want to rip this apart completely - can you think of solutions to these issues?