Path MTU detection is all sorts of fragile, so exposing a tcp maximum segment size implying a MTU above 1500 is asking for trouble; actually even just 1500 isn't always a good idea [1]. There are many networks where too big packets are dropped without notifications, and if the other end is also on a 9000 MTU LAN, then you can get stuck. sigh
On the host side, packetization is not that big of a deal; nics can help, but it's also just not that many packets. Where hosts tend to run out of cpu is when you're dealing with much smaller packets.
Larger packets could help routers of course. And larger packets would probably mean fewer acks, which would be nice too. But, it's unlikely to happen unless mtu probing is enabled in more places.
[1] The best is to send the lesser of (theirs - 28) or your actual value. Well best is relative, this will result in the most successful connections, at the expense of more packets for networks where people aren't insane.