I'll start by agreeing that also knowing judo, grappling or striking would greatly benefit an aikidoka, just as cross-training done right can benefit any martial artist. However, I strongly disagree with the following assumption:
he taught with the assumption that most students already had some basics (striking, clinch, close grappling). Aikido's techniques make more sense as a system under that assumption, IMO.
While I understand why one would make such a statement, it runs counter to the documented history of aikido and I think that it cannot reasonably be considered a credible hypothesis, for the following reasons (I could think of more):
1) Ueshiba himself had relatively little martial experience besides his Daito-ryu training and had certainly not mastered any style besides daito-ryu. Daito-ryu aikijujutsu was the only martial art that he studied in depth and what he taught was simply his own spin on the topic (with a rearranged curriculum, a slightly different stance, etc.). It seems strange to me that he would teach it as a "finishing school" for already accomplished martial artists while he himself became the best in Japan almost with Daito-ryu alone. Likewise, Yukiyoshi Sagawa displayed abilities similar to Ueshiba's and he exclusively trained Daito-ryu from age twelve onwards.
2) While a lot of Ueshiba's disciples had done judo, there are also numerous disciples that had no other martial background. To cite a few, Kuroiwa joined after a couple of years of boxing in highschool (and became famous for his dangerous aikido hip throw), Tada had learnt archery, Saito had learnt kendo and some one year of highschool karate, Tadashi Abe joined at 16 and Isoyama at 12! Ueshiba taught a wide range of students, including women and children, and he could not possibly presume that all his students had the basics Gerry described. What's more, there is no record of him teaching such students those alleged basics nor delegating this task to any senior student.
3) None of Ueshiba's disciples "completed" their aikido teaching with another martial art (with maybe Mochizuki being the exception) so none of those thought that it was necessary to have a previous background in another martial art to effectively learn aikido. Some of them did teach strikes as they were done in aikido kata but, to my knowledge, none of them thought necessary, for example, to incorporate the karate kihon or kata.
4) When his students would play judo after hours, Ueshiba would storm out of the dojo and tell them to "stop doing this chink stuff" (in reference to the legend according to which the founders of the lineages that made up judo both studied with Chinese). Leaving alone the fact that he seemed to despise judo, if the quoted assumption were true it would be strange that he would prevent his disciples from practicing the very basics his system was supposed to build upon.
5) I have watched a lot of videos of randori from the old timers (Ueshiba himself, Saotome, Shioda, Chiba, Shibata, Tohei, etc.) and I have not found any video where the aikidoka uses a move from judo or karate, for example. Interestingly enough, most moves are not even following aikido kata: we see a lot of preemptive strikes, counterpunches, body drops, formless rooted strikes (including strikes with the hips or shoulders), formless throws regardless of where one is grabbed...
I believe that the system is meant to condition and engrain a series of attributes within students (such as grounding, distance, timing, generation and transfer of power to any part of the body, ability to find an opponent's center and take him off balance, etc.) so that they can be used in such a free form and, if an opportunity for a technique (lock or formal throw) appears, why not? This is reflected all throughout the system itself and in the founder's teachings such as his emphasis on formless "takemusu aiki" or his famous quote, "aikido is 90% atemi". This video is a good illustration, albeit the uke are not fully resisting:
