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Their fairly unique way of gathering Food is actually a double-edged sword: on the upside, they do not need to waste early resources and time when building Farms, saving them a good amount of Timber, which can be used otherwise (Markets, Temples). On the downside, the gather rate cannot be increased in any way, often resulting in a poor Food production in the mid to late game - unless they have access to other sources of Food (however, Fishermen get nerfed as well, see below).
As the Lakota cannot build or capture Granaries, they cannot research Granary upgrades (thus no increase in Fishermen's Food production as well) or Medicine technologies - denying them any improvements for garrisoned unit's healing as well as production time and vision range for Barracks and Stable units. The latter one is made even worse by the fact, that much of Lakota's powers revolve around fielding lots of Stable units.
However, when conquering a city, instantly destroyed Farms and Granaries can be useful to some extent. The enemy may not want to retake that city as they would have to reconstruct the aforementioned civic buildings.
The freedom concerning building and city construction sites has its limits as well: while they can construct early cities almost everywhere, building them far away from the capital usually proves to be a bad idea, as they can become pretty hard to defend. Also, to create new cities on other continents, the Lakota still have to develop Commerce Level 2 (Coinage), which unlocks colonization. The good thing about the Lakota's power is that when playing on warring states and there are too many nations you can pull your self out of there and rebuild your country on another continent. The Lakota's construction power still has some uses: Bringing some workers along with your army allows you to quickly raise a Barracks or Siege Factory to reinforce your troops - far away from your territory. Also, you can try to secure remote locations with a Fort or Tower, like an important rare resource.
The invisible borders and territory does nothing except irritating human players, rendering it a more or less useless feature.