Competing on price is entirely possible and feasible. What it boils down to is understanding how that affects your positioning (i.e. being known to compete on price) and how that affects your value proposition (if your only value add is price, then you're commoditising your productivity).
To put it another way, Ryanair compete on price and routinely gouge their customers, but they still have them. EasyJet competed initially on price without (initially) gouging customers and took large sections of the UK domestic and short-haul business market. British Airways are now struggling to keep afloat as their cost structure is no longer competitive.
If you're going to compete on price you need to have some very rational and thought out plans as to how you intend to compete on price and for how long. When we started doing penetration tests in Local Authorities at Mandalorian (where Local Authorities have been told to cut around %20 in costs overall) we deliberately sold at a lower rate in order to capture specific key councils in specific regions, so we could use them as case studies to go after the rest in that region. It didn't fundamentally affect us (other than not being sexy work) as what we lost in profit we made up for in volume. Now we have sufficient presence in that market to bring our prices back up to what the market will bear, and we have a good pricing strategy to boot with a low cost base.
At 44Con we originally didn't have a hotel to host the event (or speakers for that matter), but needed to raise funds for the deposit. We started selling early bird tickets at a discounted rate in order to raise funds instead of taking a loan from the bank, and it was much more successful. That, combined with sponsor funding has meant that we'll be in a better position next year to enter venue negotiations for the next 44Con.
The bottom line is that as a startup you won't have a brand and competing on price is a potential route to revenue while you have a low cost base. If you're close to ramen profitable but need revenue quickly, lowering your prices can work as a strategy providing your volume increases and you know what your costs are (and aren't making a loss in the process, at least unless you have cash to burn). Competing on pricing in an established market is absolutely the right thing to do and the easiest way to disrupt while your MVP is still being built or has only just shipped.