Valmorna - I have yet to see the purpose of the silent g in Turkish (ğ); the hat on a (â) has been done away with (by Government edict). The few words, as you precisely point out, that have vowels together are foreign, despicable words like saat (Time - Persian) and maas (salary - Persian), and the frequently-heard Maalesef (unfortunately - Arabic).
When Atatürk (PBUH) brought in Latin script in c 1928, he could have got rid of the weird vowels and consonants that existed in spoken Turkish, whilst he was at it: İ ç ğ ı ö ü ş
Sadly, he didn't, thus the oft-heard Erdogan on Western media.
Remind me to get out more!