It is saying that although traditional food tastes really good and is enjoyed by the people who grew up eating it, many people want 'fashionable' food and so because the traditional recipe might not use fashionable cooking methods/ingredients, it would not be considered as 'good' by those people or be as popular as dishes which use the latest cooking methods and ingredients.
If something is 'celebrated' in this context, it means that many people say how good it is.
'To cut it' means to be considered good enough for a certain situation. E.g. if you think about football, you might say 'that player is good, but he just can't cut it in the Premier League'.
Hope this helps.
Ellie.