I understand that the effect of certain spells, once cast, cannot be moved around. A Web for example, is all sticky, a stonewall is not going to move...
However, the Insect Plague spell, which my Mummy Lord cast, seems to be static too even though is composed of flying locusts. So once cast somewhere, it is not going to move anywhere. Only the spell does not really say one way or the other.
Is there a place where RAW indicates that spells such as that one can or cannot be moved?
AOE spells can only move with their points of origin, unless the spell's description explicitly separates the effect from the point of origin.
AREAS OF EFFECT
Every area of effect has a point of origin, a location from which the spell’s energy erupts. The rules for each shape specify how you position its point of origin. Typically, a point of origin is a point in space, but some spells have an area whose origin is a creature or an object.
An AOE that is centered on a creature/object can be perceived to move easily because a creature/object moves easily relative to the planet. An AOE that is centered on a point in space is much harder to move because such an origin is usually part of the planet, and to see the planet in motion, you'll have to be outside of it (like, in Outer Space).
INSECT PLAGUE
Swarming, biting locusts fill a 20-foot-radius sphere centered on a point you choose within range.
Unfortunately, Insect Plague is centered on a point in space. The spell's power emanates from that point, generating insects that cannot go beyond the spell's area of effect. Because the spell's description does not explicitly separate the insects from the area, then the insects cannot be moved into a different area.
Consider the Incendiary Cloud spell:
INCENDIARY CLOUD
A swirling cloud o f smoke shot through with white-hot embers appears in a 20-foot-radius sphere centered on a point within range.
The cloud moves 10 feet directly away from you in a direction that you choose at the start of each of your turns.
Now, this spell generates an AOE, but then explicitly separates the effect from the point of origin, allowing the effect to disengage and move away.
Short Answer: Yes. An area spell is static in position unless otherwise specified.
From my experience working with the usage of spells in my campaigns, I find it safe to assume that, unless specified, an area spell cannot be moved by its caster's will. Many spells drop slight hints to this in their wording. Case in point being the spell in question.
In the case of Insect Plague, I would quote one part of the spell's text that alludes to it being a static area.
Insect Plague (5th level, Conjuration) The sphere remains for the duration, and its area is lightly obscured.
Note the word "remains" in this context. If we just take that word into account, by its definition from the good ol' internet we get:
Verb : re·main /rəˈmān/ : stay in the place that one has been occupying.
We can then assume that Insect Plague does indeed stay in the same spot, immobile.
Each spell that affects an area over a duration normally specifies whether it is mobile or not, Insect Plague was easily the least clear on that if you don't read into the text too much. Especially since it's a swarm of moving insects. Let's take Control Weather as a separate example for a moment.
Control Weather (8th level, Transmutation) You take control of the weather within 5 miles of you for the duration.
This spell also specifies where the area is, in this case Control Weather is movable, but only by moving yourself. The wording in spells can be finicky. So make sure you pay careful attention to how it describes the placement of the spell. When in doubt, refer to the PHB page 204 regarding spells for extra information regarding placement. It probably does a better job than I did.
