I've never heard of a built-in encounter cooldown in Pokemon series.
I'd attribute what you're describing mainly to a confirmation bias - you're more likely to remember situations that support the idea of cooldown, rather than the ones where you've had encounter after encounter. After all, some caves are known to be a nightmare to walk through without repel.
In addition, for a major part of the game you actually walk on paths that have 0 encounter chance - you have to walk off the road and into the tall grass to even have a chance at a pokemon encounter after all - with particular areas being exception to the rule, like water or caves.
Lastly, This thread on pokemonDB explores a more technical aspect of the mechanic. While there are no encounter cooldowns mentioned, your encounter chance depends on (quoting) a formula:
P = x/187.5, where x stands for rarity of the pokemon:
- Rarity of Pokemon x
- Very Common 10
- Common 8.5
- Semi-rare 6.75
- Rare 3.33
- Very Rare 1.25
Depending on an area, a mix of pokemon rarity and a number of different pokemon influences your encounter rate. If there are only a couple of pokemon to be met in an area, encounter rate goes down. Same thing happens if some of the pokemon are rare. On the other hand, in caves you are bound to meet a high number of common pokemon, which is why you might battle every other step you take.