Moving inherited RRSP & TFSA in kind to non registered account

Recently, my mother passed away and I was the named beneficiary of her RRSP and TFSA. Her broker is recommending that we move the accounts in kind to a non registered account under my name. I currently have a RRSP of my own and a FHSA with the same broker but, have been managing my TFSA through WealthSimple and would eventually like to move my RRSP there too.

My questions are:

• When my mother passed away, were her assets deemed as sold and will be counted as income on her final tax return? I understand the TFSA portion is tax free.
• Other than staying in the market and keeping the same holdings, are there any advantages to moving the accounts in kind to a non registered account?

For context, I am planning on buying a house within the next year or so, so it would be nice to have the funds available if I need them. I'd also like to maximise my FHSA, RRSP and TFSA contributions first and it seems that moving the assets in kind to a non registered account would hinder me, as I will be taxed on my mothers TFSA.