In the third level of the dream in Inception, why doesn't Eames impersonate Robert Fischer's father to plant the idea in Robert's mind?
There is nothing concrete in the story. However it is certainly plausible that an attempt to replicate the personality and relationship with a close relative or friend in a dream might be fraught with danger.
You might easily misjudge the relationship and 'research' is less likely to reveal anything too personal you can use.
We can see hints of this in the conversation Cobb and Eames have with Saito about how to approach the problem.
EAMES How's Robert Fischer's relationship to his father? SAITO Rumor is the relationship is ... complicated. COBB We'll need more than rumor, Mr. Saito.
Eames is also able to get some face to face time with Browning, in order to capture his mannerisms. I doubt he gets more than a glimpse of Fischer himself as he is in his hospital bed in the next room, and even then he is unlikely to see the typical behavior of the man.
While inception can be done at any dream level for it to take place, you still need a really good narrative to make the inception/idea take/grow within the subjects mind.
The narrative was to trick Fischers subconscious that his father was pushing him to a different path of dismantling the company (the inception), they needed three dream levels to pull this off.
Had they used Eames to impersonate his father in any of the three dream levels, Fischers subconscious would have fought back, by either not believing the idea or his subconscious projections waking/killing the team in any of the levels.
Take for example this scene conversation:
COBB An idea Robert Fischer's conscious mind would never accept. We have to plant it deep in his subconscious. ARTHUR How deep? COBB Three levels down. ARTHUR A dream within a dream within a dream? Is that even possible? COBB Yes. It is. COBB Now, the subconscious motivates through emotion, not reason, so we have to translate the idea into an emotional concept.
Cobb also believed the only way to get Fischer to believe the inception was to make Fischer's own subconscious trick his consciousness.
EAMES Now, in the dream, I can impersonate Browning and suggest the concepts to Fischer's conscious mind... (draws a diagram) Then we take Fischer down another level and his own subconscious feeds it right back to him. ARTHUR (impressed) So he gives himself the idea.
In summary, they needed the many dream levels to build a narrative for Fischers own subconscious being able to present his father, that would then instigate an emotion triggering the idea aka inception.
Because Fischer is supposed to give himself the idea; and the best way to do that would be through his father's projection, with whom he yearned a close connection.
the best way to introduce that idea, sort of spark it up, in a particular level would be in the form of his second closest person (as far as the film is concerned), Browning. So, if Browning could somehow put that root idea in Fischer's head, then eventually Fischer's own subconscious projection would give the idea to him. That means to introduce the idea, Eames needs to impersonate Browning.
If instead, Eames impersonated Maurice Fischer, then it would be Eames who gives the idea, not Fischer Jr. himself. Which would be, as the movie states, unnatural and not very well.
There was also the fact that Maurice Fischer was in his deathbed, barely able to move, so to learn his behaviors and mannerisms (which would have changed from his younger self) would prove to be much harder for Eames.