This is a question that was asked in the Hombu dojo newsletter, "Why are there no foot techniques in Aikido?" I have heard Aikikai Shihan state "foot sweeps are for those Judo guys, we don't do them." The Hombu newsletter clarified the idea somewhat.
The article makes two main arguments. The first one being...
"One characteristic of Aikido is the absence of foot techniques and because of that, Aikido techniques attain dignity."
I think this argument is silly. Humans are too evolved to use our feet for martial arts? This argument is absurd.
The article goes on to have a somewhat more logical argument against foot sweeps.
"The other reason for the absence of foot techniques in Aikido is that they are used far from an opponent and the feet cannot reach the opponent."
This idea initially makes some sense. Aikido training tends to focus on a mid range attack. Someone is coming in from a distance and striking or grabbing in some way. At the extended range it is difficult to execute a foot sweep technique.
I find this logic is somewhat flawed. The instant a attack happens, range is broken and now the two people quickly enter a grappling range. Most Aikido training assumes successful technique and uke happily falls over. I have an earth shattering question to the Aikido community, What if attacker does not fall over and he begins grappling? Does Aikido fail here? What if the most effective and appropriate motion is to do a foot sweep? Wouldn't it be Aikido?
Aikido absolutely has foot sweeps. It has sutemi waza (sacrifice throws). It has ne waza (ground techniques)
The real reasons Aikido people tend not to do foot techniques are not because these motions are not Aikido. The reasons are...
1. Ueshiba Sensei's personal techniques did not include them. Many of his students, rather than innovating and taking aiki from other traditions have made themselves happy in photocopying one man's version of Aikido. There is a continuing fallacy in many Aikido schools. Many people believe Ueshiba's aiki was perfect and all of us are mere followers. We must try to recreate the work he did. Humbly I suggest that idea is not the true way.
2. Poor uke training. Many Aikido schools lack a system of free play randori. Instead the attacker takes a nice pretty fall every time rather than engaging on a grappling level. Realism must be a factor. The first technique does not always work! People can throw Aikido artists! Does the conflict end there?
I make no bones about it, I think there are foot techniques in Aikido. I think a good Aikido program should contain exercises that challenge the student at all ranges with a variety of problems. If an Aikido artist is not able to generalize the concepts of aiki to different problems, ranges and connections then there are weaknesses in the system. There are large holes to exploit. If an artist becomes comfortable practicing Aiki at range, in grappling and the ground...etc, then and only then Aiki becomes a true martial strategy, not a mere collection of techniques.
Here is some of our basic work at KyuRyu AikiBudo at the ashi waza range.