Some babies/toddlers suffer really badly with separation anxiety, a normal developmental phase, my dd went through this and at 2 yes is fine but often if I go off to do something she will call 'mummy where you' and then come looking, she will find me, say hello and then wander off again.
Ds2 and ds3 were both very happy to go off exploring but for a while kept me in their line of vision. At toddler groups they would crawl off then I would see therm stop and sit up and scan the room until they saw me, then they would smile and then continue with their exploring. Occasionally coming back for a cuddle or feed etc.
Ds4 was more about independent and so is did she goes off and gets on with her own thing.
But my elder ones are 13, 10 and 8 and all fine now. Can be left alone in the house, elder two can go off to town. Ds1 goes off to the city, to the cinema, blazer quest, gets buses/trains etc on his own and ds2 is gradually doing more in preparation for high school.
Their needs as babies and how responded to them has not led them to become dependent or incapable or spoilt.