I can imagine that if an account has "too many" positions and/or open orders, that then the processing of new orders can be slowed down. How is the situation with the big brokerage firms IB and TDA? Do they perhaps have some hardcoded upper limits? Can an account handle say 200 positions plus 200 not-yet-filled open orders, without degrading too much in processing speed wrt placing new orders? At what limits (s.a.) should one open additional accounts?
What you see on your side is just values that are being streamed into your frontend. You could have 100 million open orders and the connection would most likely not break a sweat given you have a decent internet throughput rate and given the updates are throttled. On the broker end they employ high performance hardware and applications that are capable of handling millions of orders, fills, position updates... Summary: you have nothing to worry in this regard. If you experience issues then the bottleneck is elsewhere.
I have ~120 open positions @ TDA (down from ~140) and 350-400 GTC orders open (down from 400-450). Recently opened an account @ IBKR with ~100 GTC orders open. No issues at either broker. Swing trading orders not scalp/daytrade.
Hmm. you are too optimistic, IMHO... It might have such big overall capacity, but what counts in practice for the trader is the share of that capacity he/she actually gets...
For options, IB limits you to orders only on one side of the book for each contract at any given time.