The missing ability was probably just another error than deliberate.
The rules say artillery needs to reload on page 14, and refernces the rules for special weapons starting on page 24 regarding the Reload action.
[Weapon]: Reload on page 21 specifies artillery often requires Reload, which indicates not all artillery does require a Reload. That contradicts the rule from page 14, but in theory, page 24 would work to clarify the disparity.
Reloadable Weapons on page 24 specifies weapons that are Reloadable are specified on the bottom of their card. If an artillery weapon requires itself to be reloaded, and does not have the [Weapon]: Reload ability, then the rules as written would mean those artillery weapons without [Weapon]: Reload could not Reload, and so become effectively limited ammunition weapons, as they could not use the required skill to Reload.
The Lothar has the required skill.
The Steel Rain has Reload for the Petard Mortar, but not for the 4.2" rockets. The fluff regarding the 4.2" rockets indicates they are too large to be reloaded during a battle, but now the NCO Command Squad contradicts that fluff, by allowing a full reload without requiring a Reload action.
The Artillery rules, as written, with the suggested requirement for always needing to Reload even when [Weapon]: Reload is not listed, do not negate the need for the Steel Rain to spend a Reload action if it does not fire all of its 4.2" rockets in one attack. The Artillery rules, as written, do not give any exception, nor do any of the rules for the Steel Rain, as they only reference its inability to reload its limited ammunition supply, so ably contradicted by the NCO Command Squad. While many players use the 4.2" rockets for a massive strike, I have seen players use it successfully for multiple attacks, as well. The Artillery rules do not specify why the Reload would be required, only that the Reload is required, as referenced starting on page 24.
If the rules from page 14 are combined with the rules from page 21 and 24, the Steel Rain can fire its 4.2" rockets as it wishes, without the need to Reload, as it is not an artillery weapon that requires Reload per page 24, and is excepted from requiring a Reload by page 21.
That consideration would make the inclusion of Reload on the Lothat's Nebelwerfer appropriate, but also show any new artillery class weapons as needing [Weapon]: Reload, or being able to fire every turn without Reload, or only once even without limited ammunition due to their inability to Reload.
Tie that with reality, where automatic loading artillery exists to match other, slow loading artillery. Fast loading artillery that is hand loaded also exists, and has existed since before WW2, so having other artillery weapons that do not require Reload would make far more sense.