I compiled all comments, and answered your comments:
Are you wanting too much? There has never been the one optimal obligatory
clearly superior solution for church architecture. Each general plan has advantages and disadvantages, besides being subject to custom and tech or $$ limits.
The church must be structurally sound, and with no modern ways to calculate stuff, they had to be conservative - extra support, wider walls, etc, especially when they wanted to go bigger, better, more amazing.
It also has to inspire, to help to elevate the heart, generally, to show an image of heaven. These two always go together. The selling spin of an architect may be a really useful idea for a preacher, and vice versa. Even the original Roman basilica basic plan is described by Vitruvius as an image of “Order, grandeur and harmony”. It was an image of the State suitable for a civic building, but isn’t this also a valid image of heaven? At least they had to make do with it, because the other common building plan, the pagan temple, was not suitable for christian worship.
The cross-shaped church with transepts was/is an option. Among others. Not different from any architectural endeavor, where the architect has to balance requisites and limitations with taste and preferences from his clients and from himself.
You could put a big tower over the crossing, but most (continental)
gothic churches have tower(s) in the west facade.
Towers involve big $$, customs… Hard to see a pattern. Probably it depends more on $$ and purpose: bells? Watchtowers? Desire to embellish more the façade to be seen from the square, or to be seen from a distance?
The transept faces can hold nice big round windows, but that alone
does not seem so important to me.
Transept can also include doors, easing faster/safer entrance/exit. Separate doors + elaborated portals + big window + separate portion of roof = more opportunity to beauty here… But, yes, it is ONE solution among various...
The transept makes the church cross-shaped, which is of course
symbolically nice. However, the cross is really only visible in the
bird's eye view or on a plan, while on the ground it is less clear and
often obscured by the buttresses, extra chapels, a cloister etc. So
it's not clear to me that this is really that important.
Com’on, even a child looks at a cross shaped church and understands the shape. From inside AND from outside. Even more when the shape is relatively simple, with no overtly elaborated external supports or arcboutants.
It makes the separation of the choir form the nave more obvious. On
the other hand, transeptless churches also manage to clearly delineate
choir and sanctuary without problem. And of course, conceptually, one
first defines the choir (I'd suppose), and then the placement of
transept and chapels follows.
Again, cross-shape is ONE solution among many. But lateral chapels are important. There were many more priests than needed for public masses. AND, many unemployed priests. Those could make a living by being paid to say private masses. To pray for the dead of some family, etc, or to the dead buried at the same chapels.
Also, in peregrination churches, a group of peregrines with a priest could use a lateral chapel. More ordinarily, a traveling priest could arrive and ask to say mass at unusual times. Or, in big priestly meetings, every priest would need to say mass, and concelebration was nonexistent or very rare. With many lateral altars, all of these issues have trivial solutions.
Lateral chapels and altars may have been an important basic project requisite, don't subestimate them.
The transept will in principle stabilize the long walls of the nave...
Again, cross-shape is ONE option to help stability, not the only one. And remember that gothic arcboutants, etc, were not available before the gothic era.
However, the transept and crossing tend to clutter the interior, which
is much cleaner without. Then, the transepts seem to create a lot of
essentially dead space where you don't see much of the mass. Many
churches have some side altars there, but at least in the churches
I've visited, it often seems like they don't really now what to do
with the transept areas (one of them may be the main entrance).
the comment about lateral chapels is valid for side altars too.
And, is dead space bad? Yes. But a little bit… It is not so bad. When you go to the mass everyday, or even every week, if one day you get behind the columns and are blind, it is not a big deal. I have done this many many times. And the older rite had even less visible parts than today’s. Moreover, I do not think zero dead space is achievable with more than one nave.
Generally, there does not seem to be a standard use for the transept
AFAIK, as opposed to nave for laypeople and choir for clergy. In the
comments, Luiz indicated that there would be groups of worshippers
which require separate seating, so maybe these spaces are not that
useless - but is that common?
I gave as examples pupils, nuns, or sick people, which do not apply to usual parochial churches. And, in some place/times during the middle ages, man and women seated separately. Then, transepts again would be ONE solution, among many.
Can’t people just follow taste or preferences, or choose one solution for no really super-intelligent reason, just because of habit, or because uncle bob’s village had a beautiful church like that?
Let's look at other options (the Roman Basilica I have already covered):
A greek cross is a much more perfect image of Ap 7: the angels from the 4 corners of the earth; the host before the lamb - it is an image of people from all directions coming to the altar of the Lamb, an image of heaven and/or of the universality of the church. This imagery is still present but less obviously in a cross-shaped church with transepts. The Gent Altarpiece has a good visual representation
And greek crosses were not as common in the West as in the East. A circular shaped church, such as the Templar churches… It still has some of the Ap 7 imagery, but it emphasizes an idea of community, of all equal brothers around the altar. Convenient for a small church for a military order. But less important for a normal church, besides the architectural difficulties to scale - who wants circular domes everywhere? Yet there are some circular churches.
Gothic: it did not fully abandon the Basilica theme, but emphasized another layer --> sursum corda, look above: verticality, lightness, and light. A cross shape would be still pretty much valid.