It may surprise some who have learned otherwise that the answer is actually yes (though with some nuances). While copies of the LRP given to Neophytes do not reference the Elements at all, calling these simply an "Invoking Pentagram" or "Banishing Pentagram" (which makes sense, given they have not yet experienced the Elemental Grades), Adept material does refer (either explicitly, or by intimation) to the LRP Pentagrams as being of Earth.
For example, here is a description from Ritual B (Ritual of the Pentagram):
"In the Invoking Pentagram of Earth the Current descendeth from the Spirit to the Earth. In the Banishing Pentagram the Current is reversed. The Sigil of [Taurus] should be traced in the Centre.
"These two Pentagrams are in general use for invocation or banishing, and their use is given to the Neophytes of the First Order of the G.D. in the Outer under the Title of the Lesser Ritual of the Pentagram."
And further, from Ritual C (Ritual of the Hexagram):
"And the Hexagrams of [Saturn] may be used in general and comparatively unimportant operations—as the Pentagrams of [Earth] are employed in the Lesser Ritual of the Pentagram."
This latter quote is important, because the connection with Earth is made more explicit, but we also see a comparative use of Saturn Hexagrams in the LRH. Clearly there is a "default" form that serves for use in generic circumstances.
Now, we might think the matter resolved, but clearly there is a distinction between this form as given to Neophytes and the form used by an Adept for working specifically with the Element of Earth, where the Symbol of Taurus is drawn, Earth Divine Names vibrated, Zelator Sign given, etc. Those additional associations create a much more specific (and potent) energy that pinpoints the Element of Earth in particular, as opposed to its generic form for unimportant work. Likewise for Saturn Hexagrams that employ the Saturn Symbol, etc.
One way of looking at this is that it depends on the perspective of the initiate. From the perspective of the Neophyte, who is not privy to the Elemental associations of the Pentagram (notwithstanding the fact that nowadays this information is widely and publicly available), and has not undergone the Elemental Grades (so has not seen the Pentagrams drawn by the Hierophant there, if they even noticed what they were), then the Pentagrams have no Elemental associations. From the perspective of the Adept, however, the information available becomes more substantial, and it is clear that these are drawn from or to the Earth point, even if they lack the additional associations one would add for the more specific energies of Earth in Adept rituals.
Another way of seeing this is in the (perhaps unsatisfying) vein of a "yes and no" answer. It is Earth in the sense of how it is drawn and in the catch-all, generic associations of the Element, but it is not Earth in the sense of the specific Earth energy (devoid of the other Elements) that an Adept may wish to work with.
So, why Earth? There are many potential explanations for this, but I think the most likely reasoning for this choice was quite simple: because it is the Element closest to us, the one we are most familiar with, and the one which is least volatile. There are also teachings that the Element of Earth incorporates the other three, being, as it were, the fusion of or result of them all. It therefore is the most appropriate for use for general purposes.
This might also then beg the question: why Saturn for the Hexagram? This is perhaps less clear, but I think a good explanation is the fact that the Saturn point alludes not just to Binah, but to Da'ath and the entire Supernal Triad. In this sense, the Saturn Hexagram also represents a merging of forces, and one can perhaps see why this form might also be used for general purposes.
Further, the Pentagram can be used to work with Zodiacal forces (drawing from or to the point of the associated Element, but using the Symbol of the Zodiac in the centre instead). Likewise, the Hexagram can be used to work with Sephirothic forces. There are myriad potential, specific uses, which require augmenting the procedure—in which case a single form of the Pentagram or Hexagram (or any Symbol in the G.D. system) may serve multiple purposes. It is not, as it were, black and white.
A further point for reflection: in the Elemental Grade Rituals, 2=9 through 4=7 use Equilibrating Pentagrams in addition to their Elemental Pentagrams, but 1=10 does not (more closely matching the LRP). Presumably this indicates that Mathers did not consider the Earth Pentagram as needing Equilibrating, and thus we can perhaps again see an inkling into why this particular form was given as a basic ritual to Neophytes. There is also a very clear shift in structure for 1=10 as a whole compared to the other three Elemental Grades, which is worth reflecting on.
As for why we do not use different Elemental Pentagrams in the different directions (another common question), it is simply because this is a basic, generic ritual (for the purposes of protection, cleansing a space, acquiring Spiritual Force, etc.). The Supreme Ritual of the Pentagram gives multiple modes of use for those more specific uses, working with one or all Elements. The Neophyte, having not undergone the Elemental Grades, would not be deemed to be ready to do that higher, more specific work (which is only done with a particular purpose in mind, not simply as a routine, unlike the Lesser Ritual of the Pentagram).
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