Technically, underhand bowling was allowed by the Laws of Cricket at that time. But it was considered unsportsmanlike well before the incident happened. After all, cricket had evolved from underarm to round-arm to over-arm bowling in the 19th century itself - more than 100 years before the Chappell incident. Soon, the Laws were modified to explicitly disallow it.
It may be unsportsmanlike to bowl underhanded in Tests or first-class cricket in general. But it does make for some interesting street cricket! And it seems quite natural in fact. Kids learn to throw things (not just balls) either underhanded, or over-arm with a bent elbow - not a legal bowling action either! Nobody naturally throws things in the proper cricket bowling action.
In Mumbai, much of street cricket involves underhand bowling. This may be partly because of space constraints - there usually isn't enough space for a run-up and follow-through, and pitches are well short of 22 yards too. So we used to play underarm cricket with those red rubber balls. Taped tennis balls were an alternative, but those were much more expensive, and spun less than the rubber ball. You could really give the rubber ball a rip and make it spin right across the batsman in either direction! Or you could make it dip nicely with topspin. There was also the underhand equivalent of the googly. And when there was enough space for a longish pitch, we'd permit "fast" underhand bowling. This usually involved a 3-4 step run-up followed by a rapid circular action of the bowling arm, culminating in underhand release. Although the stock delivery would be fast, full in length, and cutting into the right-handed batsman, the expert underarm bowlers were able to even bowl 'bouncers', with great shock value!
The batsman generally had very limited reaction time against such fast bowling, and a high backlift was out of the question. Most of the strokeplay had to be in the vee, because the bowling was generally full anyway, and there was no time for the horizontal-bat shots. The bulk of the dismissals were bowled. LBWs were hotly contested, because there were no umpires of course. It was up to the non-striker and bowler to settle the issue, with the help of the keeper.
Of course, we lefties had the advantage of naturally bowling away-going deliveries (leg-cutters) to the right-handed batsman. But even if we managed to get a snick, it was usually impossible to catch; it wouldn't carry to the keeper or slips. So we had to hope for the perfect jaffa, bowling over the wicket, pitching on the leg stump and hitting off. Of course all this changed if the "one-bounce rule" was in effect, that is, a catch taken on the bounce is considered legal. We called it "one-tup out" or "ek-tappi out", and it forced the batsman to try and place the ball between the fielders.
The strokeplay in general was fast and furious in such games - no scope for delicate glances and flicks. The rubber ball does fly nicely off the bat, which helps. But there's also a lot of furious running between the wickets. We usually played one-innings matches, without over limits; they weren't necessary because teams were small (5-6 players to each side) and wickets fell regularly. Great fun, and nothing underhand about it!