Well bare in mind that the Yeerks didn't actually need all of us they intended to breed like mad just to fill all our heads. I believe they may have needed a few hundreds of thousands, they hoped for a couple million but billions were more than they could really handle. To them were as six billion dollars would be to most anyone else, sure we'd like to have that much money, our imaginations go to work right away thinking of all we can do with that much money, but over a lifetime most sensible people wouldn't need six billion dollars, probably wouldn't be able to spend six billion dollars without making ridiculous purchases, but still offer almost anyone on this board alone six billion dollars in a totally legal (or maybe even illegal) way and you'd hear a lot of cries of "yes please!"
If the Yeerks came to say, the governments of the world and made a peaceful offer of exchange, Yeerk (and by extension Andalite) technology in exchange for human hosts the governments could give them prison inmates who've been sentenced to life (thus they no longer cost the government anything, families could communicate with any who survive the Yeerk v Andalite war via holograms and never know it if we wanted to get fancy, or just be told they're in solitary confinement if we dont) and the Yeerks could give us simple technology, like drop shafts and such which would be slowly intorduced to the public so no one knew there was any secret alien conspiracy.
Now there are a lot of people in prison in America but probably not enough for the Yeerks, but if every country all over the world complied to this in addition to say, networks like The Sharing which recruit voluntary hosts outside the prisons the Yeerks could have done exactly what they wanted, which is have a host which exists in mass numbers, reproduces quickly, comes willingly (or you know, gives its own kind over willingly) and it wouldn't cost them a single Hork-Bajir, just the blueprints for some minor technology and maybe, just to make us feel like we're some sort of badasses, a very low power dracon weapon, strong enough to kill a human or shred a tank but too weak to harm say, a bug fighter.
In this way the Yeerks could keep us happy while gaining the hosts they need to fight the Andalites and it would cost them virtually nothing, and we'd still be powerless to resist them because in addition to not knowing how many voluntary hosts are roaming around from The Sharing, even with the government knowing about the Yeerks they'd very likely keep it secret from the rest of their respecitve countries. Even if the Yeerk presence was known and publicized (which might even be better for the Yeerks because with the right spin so very many people would go voluntarily) the government wouldn't try to start something and unless the Yeerks made the first move any country that wages war on the Yeerks themselves would be quickly condemned by the rest of the world just out of fear of Yeerk retaliation against mankind in general.
I'm not sure how it is in most other countries but in US alone how many politicians would be quick to say "We are so sorry to hear about how the (oh let's just say) French fired on your bug fighters when you tried to build a new Yeerk Pool in Paris, but we would never do that, we just want you to know that not all humans are French, you have nothing to fear from the rest of the world."
And of course the Yeerks would laugh themselves silly over our use of the word "fear".
All in all I think that being public at least to a degree would have benefited the Yeerks so much more than subtle infiltration and the only reason I feel they went down the subtle infiltration road was indeed because Visser One wanted it that way for her own personal reasons.
