The BITX and the whole µBITX series was born as an SSB rig, the possibility of use for the CW is only for occasional use as well as for other ways of communication (even the ILER series does the same), both start from the concept of limiting initial costs of the rig, for different uses it is expected that it can be hacked and modified for its own purposes ...
If you have chosen a KIT you have to expect that hardware and software variants are needed to use it the way you want it, if you want a smooth rig of any kind, you can spend a thousand dollars and solve the problems.
If, on the other hand, you want a KIT for CW or other digital modes of transmission, you have to orient yourself on other products, there are several specialized ones for digital transmissions, but obviously these do not transmit in SSB ...
Like it or not, you have to choose between one and the other or adapt to modify them or spend more thousands dollars !, The choice is yours.
Cordial greetings, de IW4AJR Loris