Regarding the question that seems to lie at the core of the question; is there benefit (not necessarily actual mitsvah, since we probably arent discussing one) in making Torah study more difficult than it has to be. Even if there is, one could still wonder whether or not in a given case, the benefit outweighs the loss.
Although intuitively, I would strongly assume that there is no benefit in making study artificially difficult, there are some sources that indicate the opposite.
Regarding walking to praying in a more distant place, the Talmud (Bava Metsiah 107a) cites R. Yohanan as opining that one is fortunate to have a nearby bathroom, but not a nearby synagogue, since one receives reward for going to a further synagogue. Although he just says that one is fortunate if circumstances leave him in a position where he is forced to walk a greater distance; not that given the choice one should actually walk further.
However, the Talmud (Sotah 22a) cites an anecdote (apparently approvingly) of someone doing just that; deliberately praying in a further location. Although this is about extra effort expended on prayer, rather than study, it provides some theoretical background for the idea that study too benefits from artificial attempts at making it more difficult.
Rashi there (s.v. v'kibbul) summarises the upshot of that passage as:
למדנו שיטריח אדם עצמו במצוה לקבל שכר יותר.
Which seems to say that there is value in doing a mitsvah in a more difficult way. This would presumably include Torah study.
Indeed, referring to Torah study in particular, R. Yeshaya di Trani writes in his Tosafot to Megillah 3a, that the problem with translating Prophets into the vernacular was that it would allow people to learn it without expending as much effort. This would seem to indicate that it is preferable to study Torah in a more difficult manner, even if one would be able to otherwise more easily (he says nothing, for example, about a decreased quality in the study).
Accordingly, according to the above, it would seem likely that there would be a benefit, even to the point if being preferable, in finding information in a more difficult way, rather than in an easier way.
Regarding whether this Midrash reflects a formal mitsvah with formal parameters, or a mere exhortation, note that the classical monei hamitsvot such as Rassag, Rambam, Ramban, Yereim, Semag, Semak, Hinnukh, and R. Yeroham Fischel Perlow, do not discuss it as even a possible mitsva. Accordingly, it would likely not necessarily have technical parameters and guidelines like an actual mitsvah. Either way, all of the above stands regarding preferences in Torah study options.