I just tell you: Your E/O path is calculated for IFR conditions. If you see that there is an obstacle, if you know that it's not in your way and if you know that you can do a turn of 1 or 2 degrees even single engine (well at least I can do it, I'm not sure about the grey-haired ones), then you certainly can assume that you can make it.
I can see what you're getting at but the danger here is second guessing why your performance tables/computer produces certain configurations, limiting weights and EO instructions for a given runway and conditions. The 'obvious' obstacle may not be the only one or indeed the most restrictive.
I think I'd class an engine failure on/soon after takeoff as more of a 'heads down' manoeuvre than usual? Trying to visually avoid obstructions at low level while dealing with the effects of a power loss seems to me like a good start towards 'losing it', assuming you can even see the problem under the nose at takeoff body angle...
The probability of losing an engine in the first couple of hundred feet and being compromised in terms of obstacle clearance is very low (and getting lower). However, this rare event is what all of our performance calculations are based on.
...remember that your pilot's everyday life consists constantly of such assumptions. If you couldn't do that, you couldn't fly anymore. Or are you also one of such guys who declines a visual approach (there could be an obstacle somewhere!!)...
A very different kind of situation. For a visual approach, you have an aeroplane with plenty of energy (potential, kinetic plus whatever you need from the engines), descending (good field of view) towards a landing area. Why would you fly into something you can see?
For an EO departure, you are in a low height, high drag state trying to accelerate and climb using your remaining power source. You may have marked asymmetry to deal with plus cockpit warnings and a possible ET. Depending on when the failure occurred, your calculated clearance of the first obstacle may only be 35 feet! There is also very little you can do to improve the situation and you have to carry on as per the book and hope the engineers got their sums right. There is no go-around available: you're stuck with what you have. I would suggest that there is very little latitude for creativity here.