I've been in 12+ agent customer support teams a few times, a couple of which grew from 2-4 people to 12+ while I was there.
The hardest part about scaling support is that you need people who have SWE-level credentials and understanding, but way more interest in and patience with talking to customers than writing code, to fill the upper tier. You also need at least one manager who can keep agents focused, while also deflecting pressure from sales and whichever department is watching churn, and while also figuring out effective metrics to track actual satisfaction. NPS or thumbs up/down alone is never ever a sufficient measurement, you need user research and to build good account relationships to get actual, meaningful feedback.
You _also_ need to have enough time to train up junior support reps in domain knowledge, enough continuity in staffing as those reps get promoted to specialize them in high-touch features without leaving gaps in coverage, and simply enough warm bodies to prevent the kind of 24/7/365 on-call coverage the companies you start to attract as you scale from becoming a burnout vector for those reps.
Every rep you lose to burnout is like losing a limb. Your managers (or you as a founder/exec) have to be both willing and able to take the biggest bullets from angry customers so the reps can focus on solving problems. Conversely, you have to pay/benefit them (seniors especially) well enough so that they aren't tempted to move to SWE, because at the top of the ladder as a support IC there's nowhere else to go and you'll always be making less.
At the places where we did the best jobs keeping senior reps in place, they were more like a Justice League than an escalation vector. We let them pick the gnarly problems that interested them the most instead of assigning them out of a queue, and the problems that were so shitty that nobody wanted to take them became team efforts that none of the seniors had to shoulder alone. We also kept seniors involved in on-call coverage without making them be involved 24/7, assigning them 8- or 12-hour pager escalation shifts that raised them only when the juniors triaging on-call were fully blocked (and even then, the managers dove into the customer touch at that point to keep escalation continuity).
tl;dr: It's possible, even feasible, but you have to have a fantastic culture of collaboration in the reps, you have to spend a shitload of money on those reps over a long period of time, and you paradoxically have to convince them to keep doing this shitty job, when there are SWE teams in the same org recruiting them with relationships the senior reps have built over years of working on escalations.
You have to put the same level of focus, care, personal attention, recruitment, and rewards on your support team that you do on your R&D. Almost no company bothers with this. Especially in companies where a board or a past or future IPO are involved, execs take one look at the sticker price of doing this and balk - even if you can sell customers on that support being worth a higher price.