"But it is a shame as it means that they lose part of their cultural heritage."
Why? This focus on parents' or GPs heritage is IMV sometimes quite regressive (not saying it's in your case).
My dc haven't lost anything as the language I spoke as a 5 year old is hardly relevant to their daily experience in the UK today. In fact they win a lot by my dh and I being open minded and adapting to our current cultural and social context and integrating in our community. Not wanting to generalise but a few of the families who are fiercely multi-linguale because of their heritage have no English friends just other multicultural families or families form their home country, to me personally that would be a huge loss.
I really do not get this cultural heritage thing. Why look backwards? We are pragmatic and I'd be more than happy moving countries again and my dc learning a brand new language rather than the two I was exposed to as part of my early upbringing. However if we ended up moving to the country of my birth I'd be equally happy for them to polish one of my native languages (which they already speak relatively well).
For us life is busy, dh and i both work, dc go to loads of clubs and their experience is in the here and now, never mind any 'heritage' that may have come from my grand mother (who btw also had parents from 2 cultures, which seems to run in the family) so in our particular situation, there is no one, two three or four cultures and languages, it's an absolutely hotchpotch. which is possibly why we feel comfortable with one main language based identity.
As I said in my pp, each family is different, their dc have different abilities and as someones with a most diverse family background I am comfortable allowing the language of the country i live in to be our primary and loved means of communication, which defines our experience and family life.