From reading Diamond / Hyperstake threads small stacks and even empty open wallets help with network security, would
hard-coding some coins into all new wallets, aka the stellar minimum amount help security long term. Could be used as
a marketing point, free coins with every wallet??
Having some coins by default could easily be abused with scripts: clone VM, install wallet, transfer coins, delete VM, rinse & repeat thousandths of times per minute.
For small amounts of coins, faucets can be used (and try to prevent the above with captchas)
However, yes you are right, the more wallets online, the more secure the network is under Proof of Stake, but it should be part the reward/subsidy model that encourages to leave a wallet staking.
Of note, some PoS coins are experiment with fixed rewards rather than proportional rewards. The problem with that is that what makes PoS secure is the proportionality, which requires to have a large proportion of staking coins to perform an attack. The idea is that an attacker would then have to shoot himself in the foot, so to speak. With fixed rewards, you can stake the minimal amount on many wallets and obtain network dominance with little to no stake in the coin, just lots of wallets.