(tl;dr summary in bold)
<PERSON> wouldn't have had to merely suggest an alternative and try to persuade the others: she was the only one on the Falcon who knew where the secret rebel base was, and therefore was in control of the decision.
Clearly she made the conscious choice to use a rope-a-dope strategy. Having just witnessed the obliteration of her home by the dreaded space station, she knew full well that the same fate could soon befall any other planets--and their millions or billions of inhabitants--that refused to fall in line, so defeating the Death Star was not only vital, but urgent. Enticing <PERSON> to use it to attack their base was likely the only way to guarantee an engagement in the near future.
The secondary question then becomes "was this a foolhardy strategy?" Well, there were at least two problems with it. One is that it assumed the Empire would even use the Death Star for the attack, when a couple of Star Destroyers could presumably have been sent instead. Another, raised in the question, is that no one at that time had any idea if an attack on the battle station would have even a remote chance of success.
This would be troubling if the rebels could not evacuate Yavin 4 in advance of an attack, so you might say it was pretty flaming reckless. 865
However, I surmise the rebels did temporarily flee the (otherwise sparsely populated?) moon except for those needed in the "command center" for the attack. (Brazen retconning? Taking away some of the drama from the countdown to the Death Star's arrival? Perhaps, but I don't think this speculation is contradicted anywhere in canon.) Aside from the uncertain amount of time they would have had to load equipment onto a transport ship, it should have been quite doable considering the apparently tiny total force there (even compared to the later evacuation of Hoth). <PERSON> could thus sacrifice the secrecy of the base on the chance of the rope-a-dope panning out, without sacrificing the entire rebel force itself (Well, sorry General <PERSON>--but, hey, <PERSON> was willing to stand and die with him, and by that time they believed they had at least a fighting chance). Therefore, without going outside of movie canon the plan was clearly justified by the desperate situation. Even if for some reason they couldn't evacuate, the unprecedented and urgent threat that the Death Star apparently posed might justify the bold strategy if there were other rebel allies elsewhere. 865