Yes, you need a fast trainer to lure another fast trainer from the daily list (take into consideration that there are two types of lists as said in a post after this one). For sure someone will not get a fast trainer as a daily player if the player that he was suggested to be replaced is not a fast trainer (it is not random). The base position is a must if it is for a daily player while the recommended daily player's position is based on the position opposing the opponent's chosen strong player's position.
The bad is that a user would likely want a 18-19 y.o old fast trainer when his current one for say a position is reaching near the end of his time for use as a main squad player, but then he will not get an 18-19 y.o offer based on him but something closer to his old age. So, someone who would want a fast training player for replacing an ageing player playing in a particular position will have first to find a relatively low quality 18-19 y.o fast trainer for that same position from elsewhere like auctions or youth player.
One of the only good side of this system is that if you have a young, fast training player but who performed poorly (a flop), then the offered player as a suggestion of being an improvement over him is an option to consider (provided that you got an offer based on him). This is how I got my 7-star ST. I had a fast training but poorly performing 18 y.o 5-star ST in my team, and on a day in that same season I got offered an 18 y.o 7-star ST with PK special ability, and I bought him and the newly bought player turned out to be a good performer. But if your bought fast training 18 y.o player is performing well, then why buy another for a high price? Basically, this system offers the user to buy players that he might not need to buy at all except in certain special cases. This is just another system in this game that is nearly fully based on Nordeus' gain rather than in consideration of the needs of the user or what can help him.