It's true that Firestar punishing Leafpool wouldn't make any sense, but I think it's also important to consider when exactly the Three were born. Think about it, Leafpool—ThunderClan's only medicine cat at the time—had only recently gotten back from running away with Crowfeather, and Onestar was also determined to cut off ties with ThunderClan. Medicine cats having kits were also almost unheard of.
Stormfur and Brook, as well as Daisy and her kits, had also recently joined ThunderClan, while Brambleclaw had been named deputy without an apprentice. Recall that with the former, cats were so worried about ThunderClan becoming mixed to the point that
Mousefur called a meeting, and that the only reason ThunderClan accepted Brambleclaw as deputy was because of a sign from StarClan.
Except for Ashfur, who went as far as to accuse Leafpool of faking a sign so her sister's mate would be in a position of power.
Point is, Leafpool was pregnant during a very tense time in ThunderClan, it's no wonder she wanted to keep it a secret. Obviously Firestar wouldn't want to punish her, but in order to keep the peace in ThunderClan, it's possible he wouldn't have had much of a choice, or at least that's how
Leafpool probably saw it. At the very least, I feel like she—and perhaps even her family—would've probably had an even harder time of getting the Clan to trust her again depending on said punishment (again, she was ThunderClan's only medicine cat at this time).
Of course, the books—not even LW—actually delve into this, which is a shame as I think this would've been a better reason for Leafpool to give up her kits besides just the usual "I have a duty to my Clan" thing.