This would only be true if bitcoin were infinitely divisible.
In actuality the block reward will eventually be one 'satoshi' (one hundred-millionth of a bitcoin); then, when it's next due to be halved, dividing by 2 with a fixed precision of 8 decimal places will take the reward down to a value of zero.
Under your design, it sounds like it would very much be possible to produce a modified history that remains valid, by repeating the hash chaining process from the point of the edit. You couldn't do it un-noticed because the hashes would change, but you would still end up with a valid database entry at the end.
More to the wider philosophical point, having a single centralised server means putting trust in a single authority - I'm not talking so much about the possibility of being shut down (although that ought to be a worry for more than just criminals) but about the power, implicitly granted to whoever maintains the central database, to act as gatekeeper.
Essentially, if you're happy having a single central authority (if you're willing to trust that they'll always play fair, never try to interfere with transactions, never exploit their position for profit, never deny service to particular customers) then all the hashing and chaining is a meaningless veneer and you might as well just use Paypal. If you're _not_ happy with a single central authority then "Just use a database" misses the point entirely.
In actuality the block reward will eventually be one 'satoshi' (one hundred-millionth of a bitcoin); then, when it's next due to be halved, dividing by 2 with a fixed precision of 8 decimal places will take the reward down to a value of zero.