Kenneth Holmqvist and Jarosław Płuciennik discuss this in Conceptualised Deviations from Expected Normalties: A Semantic Comparison Between Lexical Terms Ending in -ful and -less. This is more of a formal examination than a practical one, so I should say now that your interpretation of the reason seems to be correct.
10.1. Adjectives meaning that a specified part is lacking.
[Here,] we find examples such as bloodless, brainless, earless, fingerless, finless, footless, roofless, rootless, toothless, verandaless, waterless. Here -less evokes a whole (such as body for bloodless) which is normally expected to have the lacking concrete part mentioned in the stem. It is relatively easy to predict what whole toothless and brainless refer to, even without any context. Not only do they evoke wholes which are denoted by nouns, the things that can be bloodless is a much more restricted group than the things that can be green, soft, or even beautiful.
In other words, when a speaker uses a word like bloodless, fingerless or roofless, s/he creates a very restricted context from the expected whole with the stem part missing. Although a restricted context, the whole may be a semantically rich concept, such as the war in bloodless war. The listener receiving bloodless automatically experiences the expectation of several such possible rich wholes (except for war, also body, film, victory, coup, statistics).
The reason that there are no -ful adjectives corresponding to this group of -less adjectives should be obvious: There are not many things normally without fingers that we would want to say are fingerful, so fingerful can almost only express either what is already expected and nothing special (fingerful hand; a hand with fingers) or what is a weird anomaly (fingerful house). Using fingerful is therefore pointless. Had -ful expressed a process leading to the state (as does -filled), the anomalies could have been resolved: Compare bloodful barrel to blood-filled barrel. But -ful only refers to the state itself.
Also, as we will see, -ful requires there to be a container involved, and normally these adjectival stems are not placed in containers. It is difficult to conceptualise the hand as a container that is possible to fill with fingers.
Though topless is not discussed here specifically, it is the same phenomenon at play.
Here -less evokes a whole (such as body for bloodless) which is normally expected to have the lacking concrete part mentioned in the stem.
(Topless evokes a person [whole] lacking a top [stem])
The paper has an appendixful of such words; other members of this category include lidless, spotless, treeless, etc.