I think the fence serves a purpose as a barrier, and that you need to remove barriers to progress on with the game, but personally, I would not have thought to use the word SEARCH for the fence. I would reward the player with a "HOLE" scenery object and a : success beep if they examine the fence. That's enough. Then examining the hole would give a message like "CAN'T EXPAND WITH YOUR BARE HANDS.". That lets the player know that they need a tool.
I think that EXAMINE should be the command that rewards players for inspection, except in the case of TALK (which is very natural to type when confronted with another character). Having two such commands for inanimate objects just forces the player to brute force EXAMINE and SEARCH for every object in the game. If every examine relates to a joke, a clue, or some progess, EXAMINE is fun. If it's just plain old messages, then it is slightly demotivating, even without duplicating efforts with having to type SEARCH too.
I tend to think of a restricted set of verbs (a bit like SCUMM) when it comes to designing the games. Yes, you certainly want to use particular verbs when it comes to particular actions, but try to keep it simple, and also try to anticipate all VERBS that relate to object NOUNs.