I both founded a YC backed startup and I worked at another YC backed startup and had a great experience there. Having said that, I can't say I would ever recommend a new graduate taking an offer at a startup (at least an early stage one) over an offer at a BigCo of some sort.

A BigCo will help them get hired for the rest of their career. Anecdotally, I learned and accomplished far more at startups than at Google, but anytime someone sees my resume "Google" is what they notice first and are impressed by. This sucks because early employees at a startup have so many opportunities to learn and accomplish way more than a typical BigCo employee, but recruiters can't easily filter on this like they can "Oh this engineer worked at Google - they must be good!" As a result, working at a BigCo will likely help their career more than working at a startup.

Pay and filtering out good vs bad offers is another concern. Most engineers are unfamiliar with startups, equity, preferences, cap tables, and everything else. We on HN are probably more knowledgeable, but I founded a startup and still don't fully understand it all so I can't imagine how someone completely unfamiliar with startups could possibly evaluate an offer. This is made worse by the fact that it feels like startups for the past decade have taken advantage of this ignorance and screwed over many early employees with poor offers and a fake promise of wealth when the company is a mega-success. Many others have made this point in this thread already so I won't get into the details, but the TL;DR is that employees need to be treated as vital investors in the business and as people you want to help succeed.

A third concern is development and training. At a startup you are expected to already have a pretty solid knowledge base when joining; you typically need to know how web apps work, some of the stack the company uses, etc. That isn't to say you won't learn a lot at a startup, but this is typically done in a "sink or swim" manner where you have to have some foundational knowledge to avoid drowning. At a BigCo this isn't always the case, and many new grads will be hired with less domain specific knowledge and are given an opportunity to learn and grow over the first year. Now I realize not all startups (especially early stage ones) can afford to hire employees who won't be contributing in the immediate future, so I'm not sure how you fix this (maybe a company like Triple Byte could find promising employees who lack some specific knowledge and give a crash course before sending them off to startups to interview?), but if you can get hired at a BigCo you can basically get paid to learn these skills which is a much more enticing offer.

A fourth concern I've heard from people less familiar with startups is concern that the startup will just die at any minute leaving them jobless and in a tight situation. This mostly stems from founders not sharing important information like cash reserves, burn rate, runway, etc, so I think the general fix is to encourage founders to provide more clarity around these things. The problem is this is hard because no founder wants to admit they are failing or that the company may not be alive in 3 months. They might raise money or turn things around and they don't want their best employees to leave, but by not saying anything they risk getting into a situation where employees need to be suddenly let go and a single story like this can scare away many potential candidates. This just isn't as much of a risk (or it is perceived to be less of a risk) at BigCos, even though they do occasionally close down branches.