Many natlangs have irregular verbs that do not follow the same patterns as the majority of verbs, often as a product of old verb patterns that are no longer used. Some of the benefits of not having irregular verbs are an easier to learn and interpret conlang, but are there benefits, such as giving a sense that the language has changed over time?
Irregular verbs are naturalistic.
For this reason, even an international auxiliary language, namely IALA Interlingua, has irregular verbs to match its Romance source languages (that are famous for their wealth of irregular verbs mostly directly inherited from Latin)
Irregularities add flavour to your conlang.
They make the conlang as a whole more interesting and create some esthetic effect. It also shows that the conlang designer has spent some more time to make Eir creation not too schematic.
An invented language should have in it what the glossopoet wants to put in it. Regardless of which point of the Triangle your language most closely identifies with, there is plenty of room for whatever you might want to put in there.
So, yes, indeed, be it auxlang or artlang or engelang, an invented language shòuld have irregular verbs (irregular nouns, irregular adverbs, irregular interjections, etc) if that's what is required by the language for it to be true to itself within its context and also be an accurate projection of the glossopoet's vision for it.
Yet also, no, indeed, be it auxlang or artlang or engelang, an invented language should never have irregular forms of any kind. If they cause the language to run afoul of its creator's vision for it, then they are inappropriate to the work of art being created. Or if such irregularities would in any way foul up the language's subcreated realism.
In some respects, there may be matters of taste or audience expectation involved. For example, I think most language inventors would argue that auxlangs should be as irregularity free as possible. I'd argue the opposite, but that is indeed a matter of taste and sense of plausibility. Perhaps also a nod to a future where the auxlang in question shall have conquered all others and taken its rightful place as the naturalised L2 of the entire world. Irregularities are bound to creep into such a system.
There is no particular benefit one way or the other external to the invented language. I don't think a perfectly regular system is any easier to learn. It's not inherently better to be irregularity free. Within the language, it might be argued that verisimilitude and plausibility (leastways of human language) demand some amount of irregularity. Surely that might be seen as a benefit, perhaps for a language within a fictional setting.
So, yeah. Put em in or leave em out. Dealer's choice. Six of one, half dozen of the other! There is no right or wrong answer here.
Depends on what your goal is. If you want to create an auxlang, then you should have few, if any irregular verbs. If you want naturalism, then most natlangs have at least one irregular verb, though the exact number varies widely. Also consider how your irregular verbs will arise.
A benefit to having irregular verbs in your conlang is shortening common words. If common words like "to be" and "to walk" were 4-5 syllables in some conjugations, your speakers might consider it a hassle to say those gigantic words all the time, whereas less regular, but shorter forms of the conjugations might be easier to say.
Though really, it depends on what you want in your conlang. If you're going for naturalism, some irregularities are a must, but if you're going for an auxlang, avoiding irregular conjugations (or possibly even conjugations altogether) would be ideal.