RAW, yes, and arguably now, RAI, as well
The answer provided by Rubiksmoose has been further removed from perceptions of RAW and RAI recently, since Jeremy Crawford's tweets have been declared as no longer official rulings or expressions of intent in any way, only the Sage Advice Compendium found here: https://media.wizards.com/2019/dnd/downloads/SA-Compendium.pdf
You may note that his views on the Simulacrum spell are nowhere to be found in this official Compendium. This means said statement is no longer a valid part of any official content. Even disregarding this, Crawford had actually contradicted his statement at least once himself already.
However, the Wizards of the Coast have made Errata to the Simulacrum spell that does account for the issues presented by commonly available healing: the simulacrum is now considered a construct. This invalidates most forms of healing from applying to the simulacrum, while also incidentally making it immune to certain effects. No Simulacrum of a Simulacrum, since the spell only applies to humanoids or beasts, and it's immune to spells like Hold Person as well.
The removal of Crawford's opinion as RAW or RAI, as well as the correction of the spells original text, with no Errata replacing the word can in "If the simulacrum is damaged, you can repair it in an alchemical laboratory" with must, a simple 1 word change that would solve this issue, the spell should allow healing that works on other constructs. This is definitely RAW, and the recent developments with Crawford's rulings in my opinion give a large point toward arguments of RAI.
Spells which cause a creature to regain hit points but do not specify that they have no effect on undead or constructs, as of the time of this answer's composition are: Aid, Aura of Life(can't affect a Simulacrum since it dies at 0 hit points), Aura of Vitality, Enervation, Goodberry, Heroes' Feast, Life Transference, Regenerate, Soul Cage, Vampiric touch, and Wish.