A search of TLG-e gives 5606 instances of ἔσεσθαι. -ελεύσεσθαι is found 406 times. I've been trying to find Smyth's section where he talks about future infinitives. Does anyone have other references? Here is what I've found so far. It seems the future infinitive is limited in Attic/Homeric also to after verbs of hoping and indirect discourse.
§1866c. The future infinitive is found chiefly in indirect discourse and in analogous constructions. With μέλλω, see cross1959. It may have the article ( cross2026).
§1868. The construction of verbs of hoping, etc.—Verbs signifying to hope, expect, promise, threaten, swear, with some others of like meaning, when they refer to a future event, take either the future infinitive (in indirect discourse), or the aorist, less often the present, infinitive (not in indirect discourse).
§1959 Periphrastic Future.—A periphrastic future is formed by μέλλω I am about to, intend to, am (destined) to, am likely to (strictly think) with the present or future (rarely the aorist) infinitive. Thus, ἃ μέλλω λέγειν σοὶ πάλαι δοκεῖ what I am going to say has long been your opinion X. C. 3.3.13 (cp. cross1885), Κλέανδρος μέλλει ἥξειν Cleander is on the point of coming X. A. 6.4.18, θήσειν ἔμελλεν ἄλγεα he purposed to inflict suffering B 39, ἔμελλον ὄλβιος εἶναι I was destined to be happy ς 138, εἴ ποτε πορεύοιτο καὶ πλεῖστοι μέλλοιεν ὄψεσθαι, προσκαλῶν τοὺς φίλους ἐσπουδαιολογεῖτο if ever Cyrus was on the march and many were likely to catch sight of him, he summoned his friends and engaged them in earnest talk X. A. 1.9.28.
§1999 Verbs signifying to hope, expect, promise, threaten , and swear, when followed by the aorist (less often the present) infinitive ( cross1868), have the construction of verbs of will or desire. When such verbs take the future infinitive they have the construction of indirect discourse.
§2024 Verbs signifying to hope, expect, promise, threaten , and swear take the future infinitive in indirect discourse, and the aorist (less often the present) infinitive not in indirect discourse (like verbs of will or desire, 1868, cross1999). ἐλπίζω ταῦτα ποιήσειν I hope that I shall do this, ἐλπίζω ταῦτα ποιῆσαι or ποιεῖν I hope to do this.
§2261 The infinitive with ὥστε is usually present or aorist, rarely perfect (e.g. D. 18.257). The future is common only in indirect discourse (D. 19.72).
§2269 A result clause with ὥστε and the indicative, dependent on an infinitive in indirect discourse, and itself quoted, takes the infinitive, and usually retains the negative of the direct form.
ἔφασαν τοὺς στρατιώτα_ς εἰς τοῦτο τρυφῆς ἐλθεῖν ὥστ' οὐκ ἐθέλειν πἱ_νειν, εἰ μὴ ἀνθοσμία_ς εἴη they said that the soldiers reached such a degree of daintiness as to be unwilling to drink wine unless it had a strong bouquet X. H. 6.2.6 (direct: ὥστε οὐκ ἤθελον πἱ_νειν, with οὐ retained in indirect discourse). See also cross2270 b.
So even when the principal verb takes ὅτι, as ἐννοησάτω ὅτι οὕτως ἤδη τότε πόρρω τῆς ἡλικία_ς ἦν ὥστ' . . . οὐκ ἂν πολλῷ ὕστερον τελευτῆσαι τὸν βίον let him consider that he was then so far advanced in years that he would have died soon afterwards X. M. 4.8.1.
a. The future infinitive here represents the future indicative: οἴεται ὑ_μᾶς εἰς τοσοῦτον εὐηθεία_ς ἤδη προβεβηκέναι ὥστε καὶ ταῦτα ἀναπεισθήσεσθαι he thinks that you have already reached such a degree of simplicity as to allow yourselves to be persuaded even of this Aes. 3.256. Outside of indirect discourse, the future infinitive with ὥστε is rare (γενήσεσθαι D. 16.4, εἴσεσθαι D. 29.5).
b. ὥστε with the optative in indirect discourse is very rare (X. H. 3.5.23, I. 17.11).